International Journal of Modern Physics B

The principle of detailed balance is at the basis of equilibrium physics and is equivalent to the Kubo–Martin–Schwinger (KMS) condition (under quite general assumptions). In the present paper we prove that a large class of non-equilibrium quantum systems satisfies a dynamical generalization of the detailed balance condition (dynamical detailed balance) expressing the fact that all the micro-currents, associated to the Bohr frequencies are constant. The usual (equilibrium) detailed balance condition is characterized by the property that this constant is identically zero. From this we deduce a simple and experimentally measurable relation expressing the microcurrent associated to a transition between two levels ∊_m→∊_n as a linear combination of the occupation probabilities of the two levels, with coefficients given by the generalized susceptivities (transport coefficients). We then give a second characterization of the dynamical detailed balance condition using a master equation rather than the microcurrents. Finally we show that these two conditions are equivalent to a "local" generalization of the usual KMS condition. Summing up: rather than postulating some ansatz on the basis of phenomenological models or of numerical simulations, we deduce, directly in the quantum domain and from fundamental principles, some natural and simple non equilibrium generalizations of the three main characterizations of equilibrium states. Then we prove that these three, apparently very far, conditions are equivalent. These facts support our convinction that these three equivalent conditions capture a universal aspect of non equilibrium phenomena.

A simple form of the exact renormalization group method is proposed for the study of supersymmetric gauge field theory. The method relies on the existence of ultraviolet-finite four dimensional gauge theories with extended supersymmetry. The resulting exact renormalization group equation crucially depends on the Konishi anomaly of N=1 super Yang–Mills. We illustrate our method by dealing with the NSVZ exact relation for the beta functions, the N=2 super Yang–Mills effective potential and the N=1 super Yang–Mills gluon superpotential (the so-called Veneziano–Yankielowicz potential).

We show that the equilibrium macroscopic entropy of a generic non-reversible Kawasaki–Glauber dynamics is a non-local functional of the density. This implies that equilibrium correlations extend to macroscopic distances.

This paper deals with the design of a nonequilibrium statistical mechanics theory developed to model large systems of interacting individuals. Interactions being ruled, not only by laws of classical mechanics, but also by some intelligent or organized behaviour. The paper technically shows, also by reasoning on specific examples, how the theory can be applied to model large complex systems in natural and applied sciences.

Various physical effects resulting from environmental decoherence are discussed in the algebraic framework. An example of dynamical de-quantization of a quantum particle is considered.

We have recorded acoustic signals emitted by organ pipes in a variety of experimental framework. We have analyzed the recorded sounds with nonlinear techniques in time domain. Starting from this analysis we have extracted their relevant characteristics. Finally, we have constructed simple and suitable analogical model, able to reproduce the registered waveform and sound in listening.

An estimate is presented of the angular momentum associated with the stochastic cosmic tremor, which has been hypothesized to be caused by universal gravitation and by the granularity of matter, and to be itself the cause of quantization ("cosmic origin of quantization"). If that universal tremor has the spatial coherence which is instrumental in order that the estimated action associated with it have the order of magnitude of Planck's constant h, then the estimated order of magnitude of the angular momentum associated with it also has the same value. We moreover indicate how these findings (originally based on a simplified model of the Universe, as being made up only of particles having the nucleon mass) are affected (in fact, essentially unaffected) by the possible presence in the mass of the Universe of a large component made up of particles much lighter than nucleons ("dark", or "missing", mass).

Gravitational fields invariant for a 2-dimensional Lie algebra of Killing fields [X,Y]=Y, with Y of light type, are analyzed. The conditions for them to represent gravitational waves are verified and the definition of energy and polarization is addressed; realistic generating sources are described.

In this paper we deduce, by general hypotheses, phenomenological relations which allow to compute in order of magnitude, but with sensible accuracy, the sizes of all the observed astrophysical and cosmological structures in terms of two microscopic quantities (the radius and the mass of a nucleon), and of two fundamental constants (the gravitational constant and the velocity of the light). Moreover, we show that similar phenomenological relations could rule the mechanisms of aggregations of a large class of physical systems.

We reexamine the model of matter–radiation interaction considered by Planck in his studies on the black-body problem, and point out that its consistency seems to be in doubt. The key point is that Planck's model deals in principle with a system of n material resonators interacting with the field, but in fact Planck actually deals with a single resonator, because he explicitly makes the assumption that the resonators act independently of each other, i.e. perform incoherent motions. We point out that it would be more appropriate to deal from the start with the dynamics of the complete system, and that, in view of the long range character of the electrodynamical forces, motions of a coherent or correlated type might thus be found to occur.

A detailed description of the statistical properties of a system of bosons in a harmonic trap at low temperature, which is expected to bear on the process of BE condensation, is given resorting only to the basic postulates of Gibbs and Bose, without assuming equipartition nor continuum statistics. Below T_c such discrete spectrum theory predicts for the thermo-dynamical variables a behavior different from the continuum case. In particular a new critical temperature T_d emerges where the specific heat exhibits a λ-like spike.

In spite of the recent extraordinary progresses of experimental techniques it does not seem that, after more than seventy years from the birth of quantum mechanics, a unanimous consensus has been reached in the physicist's community on how to understand the "strange" properties of quantons, the wavelike/particlelike objects of the quantum world. In the first paragraph I will briefly recall some results on the problem of decoherence in large quantum systems, which at the same time may be viewed as an attempt of providing a "realistic" physical interpretation of the standard mathematical formulation of the theory. In the following ones I will present a derivation from first principles of the Wigner representation of quantum mechanics in phase space which eliminates altogether from the theory the Schrödinger waves and their questionable properties. This approach leads to the conclusion that the wave/particle duality has nothing to do with "probability waves", but is simply the manifestation of two complementary aspects (continuity vs. discontinuity) of an intrinsically nonlocal physical entity (the quantum field) which objectively exists in ordinary three dimensional space.

The basic cluster formalism which maps the Ising model into a correlated percolation model will be discussed. More recently the extension of the cluster approach to frustrated systems, like spin glasses, has lead to the definition of a new geometrical model, called frustrated percolation. The properties of this model will be reviewed.

Consider a correlated Gaussian random energy model built by successively adding one particle (spin) into the system and imposing the positivity of the associated covariance matrix. We show that the validity of a recently isolated condition ensuring the existence of the thermodynamic limit forces the covariance matrix to exhibit the Parisi replica symmetry breaking scheme with a convexity conditions on the matrix elements.

Drawing from exact, approximate and numerical results an overview of the properties of the out of equilibrium response function in phase ordering kinetics is presented. Focusing on the zero field cooled magnetization, emphasis is on those features of this quantity which display non trivial behavior when relaxation proceeds by coarsening. Prominent among these is the dimensionality dependence of the scaling exponent a_χ which leads to failure of the connection between static and dynamic properties at the lower dimensionality d_L, where a_χ=0. We also analyse the mean spherical model as an explicit example of a stochastic unstable system, for which the connection between statics and dynamics fails at all dimensionalities.

In this paper we describe the beam distribution in particle accelerators in the framework of a stochastic–hydrodynamic scheme. In this scheme the possible reproduction of the halo after its elimination is a consequence of the stationarity of the transverse distribution which plays the role of an attractor for every other distribution. The relaxation time toward the halo is estimated, and a few examples of controlled transitions toward a permanent halo elimination are discussed.

Feynman started the theory of quantum computation by observing that quantum mechanical amplitudes cannot be simulated efficiently on a computer, since path integrals are computationally hard. Path integrals are heuristic tools for Schrödinger's hamiltonians, at least for real time dynamics. On the contrary they have a rigorous mathematical meaning for quantum systems which are worth a finite but no matter how large number of qubits.

Feynman's model of a quantum computer provides an example of a continuous-time quantum walk. Its clocking mechanism is an excitation of a basically linear chain of spins with occasional controlled jumps which allow for motion on a planar graph. The spreading of the wave packet poses limitations on the probability of ever completing the s elementary steps of a computation: an additional amount of storage space δ is needed in order to achieve an assigned completion probability. In this note we study the END instruction, viewed as a measurement of the position of the clocking excitation: a π-pulse indefinitely freezes the contents of the input/output register, with a probability depending only on the ratio δ/s.

In this paper we study the properties of Multiphoton Squeezed States (MpSS) obtained by homodyne nonlinear canonical transformations (HNCT), in which the nonlinear term is a cubic power of the second field quadrature P. In particular, we analyze the Hamiltonian structure and the field statistics associated with these states. Finally we provide a phase space analysis by means of the Wigner functions of these states.

Consider a quantum particle of mass M in R³, described at time 0 by a wave function ϕ(x) with dispersion Δ, interacting independently with a collection of N particles of mass m. Using only Schroedinger's Quantum Mechanics we prove that when N becomes large and m/M becomes small, and if the information at time t>0 about the N particles of small mass in negleted, the system admits a "classical" description, i.e. a description in which the coherence of the wave function over distances of the order of mM^-1N^-1Δ have disappeared. We consider this a first step towards proving that most "sufficiently large" quantum systems interacting with an uncontrolled environment admit a classical description at least for position measurements.

The quantumlike formalism in the form of Madelung fluid has been applied to describe the collective dynamics of a mesoscopic aggregate of particles in a potential field. The scheme has been specialized to the one-degree-of-freedom dynamics of a charged particle beam in an accelerator in the presence of high-order multipole nonlinearities. A hierarchy of recursive equations satisfied by the moments of the density distribution has been obtained. It has been shown that the recursion relations can be in principle solved if a finite number of the first several moments is known. Beam dynamics in the presence of octupole and decapole nonlinearities has been studied as an example, demonstrating the above scheme. It has been shown that an appropriate mechanism can be introduced to control stability and coherence of states when high-order nonlinearities have to be taken into account.

We recall the classical picture about the decoherence effects induced on a quantum sub-system by the interaction with a macroscopic environment. We discuss the need of a rigorous treatment, in mathematically reasonable models, of the dynamical process bringing the system in an entangled state with the environment. We consider a simple system consisting of two particles interacting via a two-body potential and we discuss a rigorous derivation of the asymptotic wave function of the system in the limit of small mass ratio. We apply the result to the explicit computation of the decoherence effect induced on the heavy particle, in concrete examples of quantum evolution.

We study diluted spin glass models in arbitrary dimension, where each spin interacts with a finite number of other spins chosen at random with a probability decaying to zero over some distance γ^-1. For systems with pairwise interactions we show that the infinite-volume free energy converges to that of the mean-field Viana–Bray model,¹ in the Kac limit γ→0. For p-spin like models we get only one bound: the free-energy is bounded from above by the one of the mean-field diluted p-spin.

We investigate the general problem of how to model the kinematics of stock prices without considering the dynamical causes of motion. We propose a Markovian stochastic process which is able to reproduce the experimentally observed volatility clustering and fat tails in the probability density functions (PDF) of financial time series. More importantly, the process also reproduces the PDF time scaling, the power law memory of volatility and the apparent multifractality of the time series up to the time scale which is experimentally observable.

We argue that Josephson junction networks may be engineered to allow for the emergence of new and robust quantum coherent states. We provide a rather intuitive argument showing how the change in topology may affect the quantum properties of a bosonic particle hopping on a network. As a paradigmatic example, we analyze in detail the quantum and thermodynamical properties of non-interacting bosons hopping on a comb graph. We show how to explicitly compute the inhomogeneities in the distribution of bosons along the comb's fingers, evidencing the effects of the topology induced spatial Bose–Einstein condensation characteristic of the system. We propose an experiment enabling to detect the spatial Bose–Einstein condensation for Josephson networks built on comb graphs.

A short review is given of some research topics recently developed in the framework of quantitative finance and which can be referred to the effort of adapting methods and technologies of statistical physics to the analysis of economic systems. In particular we emphasize the role of a different, new perspective, in approaching financial problems, originated within the theory of complex systems and based on concepts like universality, scaling and correlation properties. Once applied to the time evolution of prices and volatility, this approach allows for the recognition of long-range and nonlinear effects in financial time series.

We study a kinetic model for a system of two species of particles interacting via a repulsive long range potential and with a reservoir at fixed temperature. The interaction between the particles is modeled by a Vlasov term and the thermal bath by a Fokker–Planck term. We show that in the diffusive and sharp interface limit the motion of the interfaces at low temperature is described by a Stefan problem or a Mullins–Sekerka motion, depending on the time scale.

Optimal compression and decompression of fractal images can be performed by out-of-equilibrium stochastic systems which exhibit a learning behaviour. We show how stochastic systems of this type are able to learn the structure of classical fractal images in a simple situation.

In this paper we review the predictions of the replica approach on the probability distribution of the overlaps among replicas and on the sample to sample fluctuations of this probability. We stress the role of replica equivalence in obtaining relations that do not depend on the form of replica symmetry breaking. A comparison is done with the results obtained with a different rigorous approach. The role of the ultrametricity and of other algebraic properties in discussed.

We seek to complement Nelson's work on the two-slit experiment by showing that the two-slit process, whose density exhibits the characteristic interference pattern, may be obtained as the model after the beam has reached the screen by means of a variational mechanism. The one-slit process, modeling the beam before it reaches the screen, plays the role of a reference model.

A formulation of the Quantum-like theory based on Feynman's propagator is presented for particle beams. Applications to betatronic oscillations of LHC and HIDIF show encouranging predictions.

We consider a system of N spiking neurons with random synaptic connections which take values ±1 with equal probability. The resulting system of equations has a stationary solution equal to 1 for the fraction of neurons having potential x at time t. This solution describes an asynchronous state. We study the stability of such a state in a perturbative way and find a threshold for the parameters of the model such that for values larger than this threshold the stationary asynchronous state is stable otherwise it is unstable. In other terms the stability of the asynchronous state holds only for relatively small random perturbations.

We study the magnetization of the pure states in (a suitable version of) the p-spin interaction model at low temperature. We give a rigorous proof of the phenomenon, discovered in ¹ that (very roughly speaking), at a given level of accuracy, the set of sites decomposes in a finite number of cells on which the magnetization of any different pure states are uncorrelated.

Trajectories in the space of the unitarily inequivalent representations of the canonical commutation relations are shown to be classical trajectories. Under convenient conditions, they may exhibit properties typical of chaotic behavior in classical nonlinear dynamics. Quantum noise in fluctuating random force in the system–environment coupling and system–environment entanglement is also discussed.

Sound happens in time. Human ears detect more objective regularities of a sonic flow, than those we are in general able to describe, yet. We review some studies of sound in the time-domain. Sound streams to be detected by human ears have a hierarchical organization. This can also be seen on the time-organization of entropic flow of the signal, that we choose as variable. We describe an experiment where ability to synchronize by ear a spoken signal with another signal of disturbs is matched to the entropic content of the spoken signal; i.e. the disturb is placed more precisely if it happens in areas of high entropy. This study is phenomenological.