Foundations of Quantum Mechanics in the Light of New Technology

The following sections are included:

• FOREWORD

• EDITOR'S NOTE

• CONTENTS

Remarks about gauge fields, electromagnetism and the Bohm-Aharonov effect are made, including a discussion on the relationship of Einstein's objection to Weyl's original idea with the Bohm-Aharonov effect.

Non-local phenomena in both classical and quantum theories is discussed, and it it is shown that quantum non-local phenomena have unique dynamical properties not shared by the classical phenomena. A short review of attempts to account for the A-B effect in a local approach is given, followed by a discussion that shows that these attempts are unsuccessful. A new type of non-local phenomena is introduced, and a number of new examples for both types of non-local phenomena are discussed.

Electron holography was employed to experimentally confirm the Aharonov-Bohm effect. Phase difference was measured between two electron waves passing through two spaces inside and outside a tiny toroidal ferromagnet, which has a completed circuit of magnetic flux. These measurements agreed with theoretical values within 10%. The possibility of flux quantization in h/e or h/2e units was experimentally negated, giving a further definite evidence that the Aharonov-Bohm effect exists.

Any attempt to verify that nature tolerates linear superpositions (rather than classical mixtures) of states corresponding to macroscopicaly distinct properties requires systems where (a) the motion of a macroscopic variable is controlled by a microscopic energy and (b) the dissipation is extremely low. A few special systems, in particular superconducting devices exploiting the Josephson effect, may satisfy these stringent conditions. In such systems one can look for the macroscopic analog of the α-decay of a heavy nucleus, and possibly also for that of the NH₃ inversion resonance. In both cases the effect of dissipation is crucial, and is reviewed here.

Under certain circumstances a superconducting ring containing a weak superconducting junction (a so called Superconduding Quantum Interference Device, a SQUID) has two metastable magnetic flux states separated by a potential barrier when an external magnetic field is applied of appropriate strength. If the junction has a small capacitance, at low temperatures where kT is very much smaller than the barrier height ΔU intrinsic magnetic flux transitions are observed from one metastable flux state into another and vice versa, or in other words a weak "persistent supercurrent" switches stochastically from one direction into the opposite. This flux transition mechanism at very low temperatures might be interpreted as due to macroscopic quantum tunnelling, a new macroscopic quantum effect.^1,2)

The amount of energy dissipated to heat during logical processing is most important from both philosophical and practical points of view. Simple cosiderations suggest that an energy kT, the thermal energy, must be dissipated in a logic operation. It has been shown, however, that logical operations can be, in principle, carried out in a thermodynamically reversible, dissipationless way. The closest approach to reversible computing is found among certain biomolecular reactions. Perfect reversibility implies infinite slowness; the rapid computation desired by the technologist requires ,large non-equilibrium driving forces and consequent high dissipation. Furthermore, macroscopic computational devices are characterized by frictional effects, lack of reproducibility and varied envrionments. They must communicate with one another over long distances. Strong driving forces, manifested as high voltages in electrical computation, are needed to overcome these unwanted effects. High voltages not only lead to large energy dissipation and diffcult heat removal technologies, they can have deleterious effects on semiconductor devices. Some of the extraneous effects in macroscopic systems are mitigated by low temperature, but considerable cost and time is entailed in developing new technology to utilize the advantages of low temperature operation.

A critical review of the theory of measurement in quantum mechanics is presented first, which is focused on the recent controversy between the von Neumann-Wigner theory and the ergodic amplification theory. Making the point clear through discussions on the controversy, we then describe a new version of the Machida-Namiki-Araki theory, as a solution of the problem, in which the macroscopic nature of measuring apparatus is explicitly formulated in a continuous direct sum of many Hilbert spaces and the unitarity of S-matrix of elementary interaction processes between object and apparatus systems is maintained. Within the framework of their theory, it is explicitly shown that the reduction of wave packet takes place even in the negative result measurement.

In today's words, "No elementary quantum phenomenon is a phenomenon until it is a registered ('observed', 'indelibly recorded') phenomenon, 'brought to a close' by 'an irreversible act of amplification'." In a delayed-choice experiment, one decides which of one or another complementary feature of a phenomenon the observing device will register after the development of the phenomenon is already under way. Several proposals for such experiments are reviewed.

When a delayed-choice experiment is conducted at the cosmological level (light coming to the telescope from a distant quasar by two different gravitationally-bent routes), "one-half of the ghost of a photon" can be delayed by a month or a year compared to the "other half". The circumstance raises an interesting technical question, "How can one keep one-half the ghost of a photon alive for a year?"

Bohr's phenomenon is discussed as a primordial building element for all of physics.

The purpose of this paper is to explore the idea that classical behavior can be forced upon a quantum system by a measurement-like coupling with its quantum environment. An example where such a mechanism of environment induced superselection is operating in competition with a hamiltonian evolution which in an isolated system would result in coherent quantum superpositions is afforded by recent discussions of macroscopic quantum coherence and tunneling. The possibility of existence of nonseparable correlations between macroscopic quantum observables in two different SQUIDs is raised.

A standard technique for detecting a classical force is to let the force act on a harmonic oscillator and to look for the resulting changes in the oscillator's motion. Conventional "amplitude-and-phase" methods for monitoring the oscillator's motion are limited in their ability to detect a force by the zero-point noise in the oscillator. The limit set by zero-point noise is called the standard quantum limit. Measurement techniques that can beat the standard quantum limit are called quantum nondemolition measurements or back-action-evading measurements. This paper reviews the origin of the standard quantum limit, sketches the theory of the most practical back-action-evading technique, derives the standard quantum limits on detecting forces having different spectral characteristics, and gives limits on force detection for back-action-evading measurements.

We describe an Einstein-Podolsky-Rosen-type situation with photons, and we show that quantum mechanics predicts strong correlations at-a-distance. According to Bell's theorem, such correlations cannot be interpreted with a classical-looking model in the spirit of Einstein's idea. We report on the most recent experiments on this subject, which show an excellent agreement with quantum mechanics and a clear rejection of the theories obeying Bell's inequalities.

The question of reductionism is examined in reference to the relation between the macroscopic physics and quantum mechanics. It will be shown that either the continuation of the two may be restored by a drastic amendment of the theories or else the effort of this kind should be abandoned with an eventual destruction of the entire physicalistic worldview.

The paper studies the status of the experiment and its role in the historical development of physics from early times until the present.

Since an experiment, performed in order to discover new phenomena to be comprehended by a new theory or in order to verify or falsify a proposed theory, constitutes itself a physical process whose interpretation is theory-laden, the philosophy of the physical experiment faces serious problems of a logical, epistemological and methodological nature.

A criterion of demarcation between classical experiments and quantum experiments is proposed.

The capability of neutron interferometry for the testing of quantum mechanical predictions on a macroscopic scale is discussed. Within a proper shaped monolithic perfect silicon crystal two widely separated coherent beams of monochromatic thermal neutrons are produced, which can be influenced individually by means of scalar as well as magnetic phase shifts and by static and time-dependent spin rotations. Only self-interference appears in the neutron case but the interference pattern shows influences of the collective properties of the whole ensemble of neutrons of the beam too. The following measurements are discussed in view of their relation to quantum mechanics: coherence measurements, 4π-symmetry of spinors, spin superposition and coherent energy transfer measurements.

In the neutron interferometer, the neutron wave packet is initially split into two sub-packets and then coherently recombined. The amplitudes and phases of the fringe pattern upon recombination can be changed by altering the experiments performed on the packets in midflight. Quantum mechanically, this is a straight-forward procedure. However in a realistic theory this pattern is present by hidden variables. Several types of delayed-choice experiments are described, and they are related to a one-particle version of the Einstein-Podolsky-Rosen paradox, and to limits on the locality of realistic theories.

An overview of the quantum Hall effect is presented. It includes fundamental properties of two-dimensional electrons under the quantized Hall conductance condition in semiconductor inversion layers, roles of localized states in strong magnetic fields and discussions of theoretical approaches.

A brief overview of the status of quantum mechanics is given by enumerating representative problems that concern us today. Some of these problems are of general nature, while others have to do with more specific problems, but they are all closely interrelated. They are also the problems left for the future, as our understanding of them is at best incomplete.

The perfect crystal neutron interferometer has been used continuously for test measurements on quantum mechanics. Semitransparent and chopper type beam attenuators were inserted into the coherent beams to observe the influence of stochastic and deterministic absorption on the interference pattern. Polarized neutrons were used to perform the quantum mechanical spin-superposition experiment on a macroscopic scale. These experiments were continued with two resonance coils in the beams, in which the coherence persisted, even if an energy exchange occurred with certainty between the neutron and the resonator system. A quantum beat effect was observed when slightly different resonance frequencies were applied to both beams. In this case, an extremely high energy sensitivity of 2.7 × 10^-l9 eV was achieved. Neutron spectroscopy is thus able to cover time domains from microscopic to macroscopic scales. Phase echo systems, experiments with chopped beams and multiplate interferometry are discussed as examples of forthcoming experiments. All the results obtained until now are in agreement with the formalism of quantum mechanics and stimulate discussion about the interpretation of this basic theory.

In this paper we report on experimental studies which firmly establish the polarisation correlation of the two-photon emission from the metastable 2²S_1/2 state of atomic deuterium. The two photons of the emission process were detected in coincidence. The circular and linear polarisation of a second-order two-photon emission process were measured for the first time. The results of this measurement were used to test Bell's inequality which allows a quantitative distinction to be made between the prediction of quantum mechanics and local realistic theories. It was found that the linear polarisation correlation data were in agreement with quantum mechanics and violated Bell's inequality thus rendering the local realistic viewpoint untenable. The no-enhancement hypothesis of Clauser, Horne, Shimony and Holt which states that low detection efficiency of photomultipliers will result in a bias for the sample of detected photon beams was tested by inserting an achromatic λ/2 plate in front of one of the photomultipliers. Preliminary results of tests of the no-enhancement hypothesis are again in good agreement with quantum mechanical prediction. According to a proposal by Garuccio and Selleri experiments using a third polariser to test Bell's inequality are in progress.

The A-B effect was tested under conditions where an electron wave and a magnetic field had no overlap: the leakage field was eliminated by the Meissner effect of the superconductor shielding a toroidal magnet. In addition, the electron penetration into the magnet was suppressed by covering it with a copper layer. Conclusive evidence for the effect was thus obtained by detecting a phase difference of π mod 2π between the two electron waves passing inside the hole and outside the toroid using electron holography. The fact that the phase difference equals π mod 2π exactly comes from the quantization of the magnetic flux within the superconducting covering.

Using Feynman path-integral formulation of quantum mechanics we show that exotic quantum statistics is allowed in two-dimensional physical systems, which is described by an angular parameter θ(0≤θ<2π) and intermediate between usual Bose-Einstein and Fermi-Dirac statistics. Two equivalent formalisms in terms of either topological action or multivalued wave functions are given. The present status of theoretical studies and the effort to search for realistic candidates for these peculiar quantum mechanical effects are summarized.

Quantum Mechanics is based on Complex Phases. This very important development had a complicated history which will be outlined.

The electrical resistance of small normal metal rings has been observed to oscillate as a function of magnetic field with period h/e. This is a clear manifestation of the Aharonov-Bohm effect but the difference is that it is occurring in a disordered electrical conductor. In addition, the magnetic field penetrating the wire results in a randomly fluctuating magnetoresistance. These quantum conductance fluctuations are signatures that the electrons are traversing the sample without losing phase memory. We also find that the electrons can induce voltage fluctuations at distances far away from the current paths.

The theory of novel quantum fluctuation phenomena recently discovered in small normal metal conductors is described. It is emphasized that these represent quantum interference effects which, surprisingly, are observable in disordered, macroscopic systems. The relationship of these effects to the h/e Aharanov-Bohm effect in normal metal rings is discussed.

The superconductivity induced by the proximity effect in a two-dimensional electron gas (2DEG) in the inversion layer on p-type InAs was confirmed using a Nb-InAs-Nb junction. It was also shown with a metal-insulator-semiconductor gatefitted junction that the supercurrent in the 2DEG could be controlled by the gate voltage (electric field effect). The controllability of the supercurrent is discussed considering the change in the coherence length of the 2DEG.

Two strategies for beating the standard quantum limit in preparation and measurement of optical quantum states are discussed. One is the quantum nondemolition (QND) measurement of the photon number using the optical Kerr effect. The other is the generation of number-phase minimum uncertainty states using either controlled reduction of the wave function by QND measurement and feedback or feedforward, or phase sensitive deamplification in a highly saturated laser oscillator with suppressed-pump-fluctuation.

This paper discusses the extent to which existing experiments test the validity of extrapolating the formalism of quantum mechanics to the macroscopic level, and in particular to what extent they confirm that linear superpositions of macroscopically distinguishable states actually exist in nature (so that even at the macrolevel, "realistic" classical concepts are not always applicable). It is concluded that the "Bell's-theorem" experiments can be interpreted as evidence for this conclusion only with some rather strong supplementary assumptions. On the other hand, recent experiments on superconducting devices, while affording strong circumstantial evidence in favor of the validity of the extrapolation of the quantum formalism at least to this level, do not directly test the principle of superposition of macrostates independently of this formalism. Currently envisaged experiments on such devices may, however, if feasible definitively test the principle against a large class of alternative, "macro-realistic" hypotheses.

Berry's discovery of a topological phase in quantum mechanics has led to a unified view of many seemingly disconnected topological phenomena in physics, both at the quantum and classical levels. In analogy with the wave function of an electron, the wave function of a photon can also acquire this topological phase. Here we review four recent optical manifestations of this Aharonov-Bohm-like phase. A distinction is made between classical and nonclassical Berry's phases in optics. One example of a nonclassical phase is the one associated with a cycle of Von Neumann projections. Other nonclassical phases will be discussed. A goup-theoretical analysis of classical Berry's phases for Maxwell's equations expressed as a Schrödinger-like equation for a six-component spinor is introduced.

New measurements of the anomalous magnetic moment of the electron and the corresponding theoretical calculation have reached the precision exceeding 4 × 10^-9 and 7 × 10^-9, respectively. This enables us to determine the fine structrure constant α to a precision of 8 × 10^-9. For comparison, the best measurements of α based on the ac Josephson effect and quantized Hall effect have uncertainties of 56 × 10^-9 and 24 × 10^-9, respectively. These values of α disagree by more than two standard deviations from each other. One possible source of the discrepancy is nonrelativistic quantum mechanics itself, in which the interaction with the radiation field is not properly defined. We have explored the possibility of replacing it with a low-energy adaptation of quantum electrodynamics which treats large and small length scales differently following the renormalization group concept. This formulation enables us to close a loophole in the usual argument for the exactness of ac Josephson and quantized Hall effects. It may also serve as a practical starting point for calculating theoretical corrections to these effects.

We consider here two problems of major recent interest in mesoscopic physics. We first review the adiabatic (slowly varying confining walls) approximation to the quantized conductance. We show that the corrections to this approximation are exponentially small in the smoothness parameter of the constriction. A condition for accurate quantization is given, based on the result that the reflections due to the sudden widening of the constriction (existing in real devices) would be highly suppressed if a small adiabatic widening and/or a potential barrier should precede the sudden widening. An interesting collimation effect associated with the adiabatic picture is briefly discussed. Next, we consider the problem of quantum interference in the presence of an environment, employing two approaches. One treats the problem from the point of view of the trace left by the interfering particle on its environment. The other regards the phase accumulation of the interfering waves as a statistical process, and explains the loss of interference in terms of uncertainty in the relative phase. The equivalence of the two approaches is proven for the general case. Some applications are discussed: Dephasing by coupling to a local spin, by photon modes in a cavity, including the difference between coherent and thermal states, and by electromagnetic fluctuations in metals.

A survey is given of our investigation of quantum ballistic electron transport in single and multiple quantum point contact structures. In the absence of a magnetic field the conductance of single quantum point contacts shows the formation of quantized plateaux at multiples of 2e²/h. An elementary theoretical explanation is given. In the presence of a perpendicular magnetic field a gradual transition to the Landau level quantization in high magnetic fields is observed. Electron transport in a wide two-dimensional electron gas has been studied with two adjacent point contacts. As a result of the selective population and detection of Landau levels by the QPCs, combined with the adiabatic transport in high magnetic fields, an anomalous quantum Hall effect was observed. Finally, the one-dimensional transport in edge channels has been employed to fabricate a one-dimensional electron interferometer. Large oscillations are observed in the device conductance due to the resonant transmission through discrete electronic states.

The search for coherent quantum oscillations in a macroscopic system is possible only if the dissipation in the system is extremely low. We have determined the intrinsic dissipation in high quality Josephson junctions from measurements on the switching of the junction into the zero voltage state. We predict from this data that an rf SQUID device and associated measurement circuit containing low dissipation junctions can be used to search for macroscopic quantum coherent effects at experimentally attainable temperatures.

We have carried out a series of experiments with one-dimensional arrays consisting of many (up to 23) tunnel junctions Al/oxide/Al with areas as small as ~0.006 µm² at temperatures from 4 to 0.05 K. The experiments have given at least two results which we believe are of a fundamental importance:

i. The first convincing evidence of the time correlation (coherence) of the single electron tunneling events, i.e., of the so-called SET oscillations of a frequency f_s fundamentally related as f_s=I/e to the dc current I.

ii. A strong evidence that a tunneling electron can probe its electrodynamic environment at distances much larger than cτ_t, where τ_t, is the "traversal" time of its passage through the energy barrier.

Boundary conditions of a superconducting wave function and a profile of pair potential near and at the semiconductor-superconductor (n-Si-Nb) interface have been studied by Andreev reflection spectroscopy. Specimens with a point contact of about 80 nm in width are fabricated using microfabrication technologies. The pair potential at the semiconductor-superconductor boundary and its dependence on the carrier concentration in the semiconductor was measured for the first time. About a 15% enhancement of the pair potential in the n-Si at the boundary is observed by increasing the carrier concentration in the n-Si from 1 × 10²⁵ m^-3 to 1 × 10²⁶ m^-3. The profile of the pair potential shows a steeper change near the n-Si-Nb boundary.

We review our recent work on the one-atom maser. We propose and analyse an experiment based on this maser and designed to probe the way in which the measurement process, that is, the presence of a detector influences the investigated quantum system. Phase transitions between chaotic and ordered structures of ions stored in a Paul trap are analysed.

We sketch a quantum-mechanical framework for the universe as a whole. Within that framework we propose a program for describing the ultimate origin in quantum cosmology of the "quasiclassical domain" of familiar experience and for characterizing the process of measurement. Predictions in quantum mechanics are made from probabilities for sets of alternative histories. Probabilities (approximately obeying the rules of probability theory) can be assigned only to sets of histories that approximately decohere. Decoherence is defined and the mechanism of decoherence is reviewed. Decoherence requires a sufficiently coarse-grained description of alternative histories of the universe. A quasiclassical domain consists of a branching set of alternative decohering histories, described by a coarse graining that is, in an appropriate sense, maximally refined consistent with decoherence, with individual branches that exhibit a high level of classical correlation in time. We pose the problem of making these notions precise and quantitative. A quasiclassical domain is emergent in the universe as a consequence of the initial condition and the action function of the elementary particles. It is an important question whether all the quasiclassical domains are roughly equivalent or whether there are various essentially inequivalent ones. A measurement is a correlation with variables in a quasiclassical domain. An "observer" (or information gathering and utilizing system) is a complex adaptive system that has evolved to exploit the relative predictability of a quasiclassical domain, or rather a set of such domains among which it cannot discriminate because of its own very coarse graining. We suggest that resolution of many of the problems of interpretation presented by quantum mechanics is to be accomplished, not by further scrutiny of the subject as it applies to reproducible laboratory situations, but rather by an examination of alternative histories of the universe, stemming from its initial condition, and a study of the problem of quasiclassical domains.

Following the past twenty-year evolutionary path in the interdisciplinary research of semiconductor superlattices and other quantum structures, significant milestones are presented with emphasis on experimental achievements in the physics of reduced dimensionality associated with technological advances.

This short note is closer to an annotated bibliography, than to a real review. We allude to reversible computation, but do not repeat the many existing discussions. We point out that minimal energy dissipation requirements in classical measurement and in the communications channel are now understood as a result of the insights gained from the studies of reversible computation. In all three areas (computation, communication, and measurement) dissipation can be made as small as desired, per step, as long as information is not discarded. Erasure of information is not essential in computation or communication, but is needed to reset the meter after measurement. We speculate on the implications for physical law, arising from the likely limited computational recision available in the universe. We become even more speculative, and suggest that the ultimate physical laws, as a result of their limited precision, have something akin to a built-in noise source, and that this is the ultimate source of irreversibility.

The proposal of 'reversible logic scheme' was motivated by two hypothetical inevitable problems in irreversible logic devices related to heat generation. A quantum flux driven irreversible logic device called QQ will be used as a counter example to refute such hypothetical problems. Thus the 'reversible logic scheme' which is highly redundant seems to be an unnecessary complication and not necessarily be relevant to the issue of null heat computing.

REFERENCES

In this talk I review the progress made over the last decade or so on the effect of dissipation on the quantum-mechanical behavior of a macroscopic variable, in particular in situations involving tunnelling through a classically impenetrable barrier. I first place the question of dissipation in the context of quantum measurement theory, and emphasize the importance of the distinction between the "adiabatic" and "dissipative" aspects of the coupling of a macroscopic variable to its environment. Next, I consider a possible theoretical framework for the problem, with particular attention to how far the necessary input parameters can be deduced from the purely classical behavior of the system in question. I then review the theoretical results obtained within this framework for the effects of dissipation both on the decay of a metastable state ("macroscopic quantum tunnelling") and on the coherent oscillations of a macroscopic two-state system ("macroscopic quantum coherence"). Finally, I discuss the extent to which recent experimental work on superconducting devices and magnetic systems has confirmed the basic assumptions of the theory.

Protons or positive muons trapped in interstitial sites in metals tunnel into neighbouring sites at low temperatures. The metalel eletrons form a screening cloud around the particle. When the particle tunnels into a neighbouring site, the electrons cannot follow the particle adiabatically. This is because low energy excitations of the metal electrons are too slow to respond the particle's motion quickly. This non-adiabatic effect results in a renormalization of the tunneling integral, which turns out to vary as a power of the temperature. Such a power law has been observed for the positive muon in Cu and other metals. For the proton in a Nb-O system a detailed comparison has been made between inelastic neutron scattering experiment and a theory which takes full account of the mentioned effect.

The superfluid model of large amplitude nuclear motion allows for a unified description of the variety of tunneling phenomena found in nuclear physics. The model will be shown to provide a quantitative account of exotic decay, of the depopulation of superdeformed bands, of the restoration of the parity in octupole deformed nuclei, of the decay of K-isomers in rapidly rotating nuclei and of the energy of coexistence for spherical and deformed states in light and medium heavy nuclei as well as the energy systematics of low-lying surface vibrations in nuclei. It will be concluded that plastic nuclear behaviour is intimately connected with nuclear superfluid tunneling. The model is also applied to the Coulomb explosion of sodium metal clusters.

Vortices and single charges have particle-like properties when they are excited in a medium with extremely low damping at low temperatures. We have experimentally studied the behavior of arrays of superconducting islands, weakly coupled by high quality, small capacitance Josephson tunnel junctions. In the islands, the phase of the order parameter and the electrical charge act as conjugate variables. The response is determined by the ratio between the Josephson coupling energy E_J and the charging energy E_C. For E_C/E_J<<1 vortices are the dominant excitations; for E_C/E_J>>1 single charges are dominant. We have observed the phase transition as a function of E_C/E_J from superconducting to insulating behavior in zero applied field. It is also possible to observe the phase transition induced by a perpendicular magnetic field, characterized by Bose condensation of vortices. We have studied vortices as ballistic particles. Recently we have obtained first indications of quantum interference of vortices.

The Hall effect for disordered superconducting films in magnetic field is discussed, with special focus on the vicinity of the magnetic field-tuned superconductor–insulator transition. Evidence is presented that upon ensemble averaging this transition possesses a "hidden" particle/hole symmetry. This symmetry implies that right at the transition the Hall resistance vanishes. Relevance to recent experiments is discussed briefly.

We study the superconductor-insulator transition of a 2-dimensional Bose-Hubbard model, considering as a physical realization an array of Josephson junctions. Within a coarse-graining approach we derive an effective free energy functional, from which we determine the phase-boundary. It also allows us to calculate the electromagnetic response as a function of temperature and system parameters, magnetic field, and chemical potential. The conductivity is characterized by an excitation gap in the real part, whereas the imaginary part behaves capacitively. Under special conditions a universal conductance appears at the transition. Qualitatively different results are obtained for frustrated and unfrustrated systems.

In spite of rapid progress of scanning tunneling microscopy in various fields of application, its microscopic basis is not obvious. In the present article, based on the first-principles local density functional calculation of electronic state various aspects of STM have been discussed. In particular, the effect of microscopic state of the tip is clarified in detail. Further, some interesting issues of the tunneling in STM, such as coherence of the multi-tip, inelastic tunneling, photon emission, Coulomb blockade are investigated.

The magnetic relaxation of a set of small ferromagnetic particles of TbCeFe₂ of mean diameter 150A has been measured near the coercive field, at low temperatures. The magnetic relaxation is thermally activated at high temperature and becomes independent of temperature below the crossover temperature, Tc=0.6K. All the results obtained at low temperatures are consistent with theoretical predictions of Macroscopic Quantum Tunneling (MQT) with weak dissipation in a ferromagnetic system. Two other examples of macroscopic systems with strong dissipation effects are also descibed.

The following sections are included:

• INTRODUCTION

• THE ROLE OF THE STATISTICAL ENSEMBLE

• LEVEL CORRELATIONS AND ORBITAL MAGNETIZATION: AHARONOV-BOHM CYLINDERS VS. QUANTUM DOTS

• TYPICAL CURRENT: THE EFFECT OF ELECTRON-ELECTRON INTERACTION

• REFERENCES

Flux lines penetrating superconducting films were directly observed using several techniques with our holography electron microscopes: First, flux lines sticking out from a superconducting Pb film were dynamically observed by an electron beam incident parallel to the film surface when they were thermally activated or driven by an applied current. Second, a two-dimensional array of flux lines was dynamically observed by an electron beam penetrating the film. The motion of individual flux lines was observed for the first time when the film temperature increased near the critical temperature, or magnetic field suddently changed.

The core states of individual vortices are imaged with a low temperature scanning tunneling microscope on 2H-NbSe₂. The quasiparticle wavefunctions of different energy are highhghted by tunneling at various bias voltages. The sequence of different energy bound states wavefunction images reveal a continuously evohing star shaped pattern. If the magnetic field is applied at an angle a "comet" shaped structure is observed. These patterns are consistent with previously acquired spectral evolution data, and may result from the anisotropy of the band structure.