Narrow Results

Starting from the notion of algebraic hidden processes introduced in Ref.9, we propose a definition of quantum hidden Markov process which extends the notion of quantum Markov chain (QMC) in the same sense in which classical hidden Markov processes (HMPs) extend classical Markov chains. We give several structure theorems for this new family of quantum states which shares with the QMCs the unique property that the finite dimensional joint expectations are explicitly given without these states being linearly equivalent to product states (as the Gaussian ones). The special feature of this new class of quantum states is best exemplified by looking at their restrictions to diagonal sub-algebras: we prove that they lead to a new family of classical stochastic processes that generalize in a non-trivial way the classical HMPs.

We prove an adiabatic theorem for the evolution of spectral data under a weak additive perturbation in the context of a system without an intrinsic time scale. For continuous functions of the unperturbed Hamiltonian the convergence is in norm while for a larger class functions, including the spectral projections associated to embedded eigenvalues, the convergence is in the strong operator topology.

We clarify the role of the Born rule in the Copenhagen Interpretation of quantum mechanics by deriving it from Bohr's doctrine of classical concepts, translated into the following mathematical statement: a quantum system described by a noncommutative C*-algebra of observables is empirically accessible only through associated commutative C*-algebras. The Born probabilities emerge as the relative frequencies of outcomes in long runs of measurements on a quantum system; it is not necessary to adopt the frequency interpretation of single-case probabilities (which will be the subject of a sequel paper). Our derivation of the Born rule uses ideas from a program begun by Finkelstein [17] and Hartle [21], intending to remove the Born rule as a separate postulate of quantum mechanics. Mathematically speaking, our approach refines previous elaborations of this program — notably the one due to Farhi, Goldstone, and Gutmann [15] as completed by Van Wesep [50] — in replacing infinite tensor products of Hilbert spaces by continuous fields of C*-algebras. Furthermore, instead of relying on the controversial eigenstate-eigenvalue link in quantum theory, our derivation just assumes that pure states in classical physics have the usual interpretation as truthmakers that assign sharp values to observables.

An algorithm and a computer program in Fortran 95 are presented which enumerate the Hugenholtz diagram representation of the many-body perturbation series for the ground state energy with a two-body interaction. The output is in a form suitable for post-processing such as automatic code generation. The result of a particular application, generation of LATEX code to draw the diagrams, is shown.

We review an event-based simulation approach which reproduces the statistical distributions of wave theory not by requiring the knowledge of the solution of the wave equation of the whole system but by generating detection events one-by-one according to an unknown distribution. We illustrate its applicability to various single photon and single neutron interferometry experiments and to two Bell-test experiments, a single-photon Einstein–Podolsky–Rosen experiment employing post-selection for photon pair identification and a single-neutron Bell test interferometry experiment with nearly 100% detection efficiency.

In this paper, Parikh's recent work, which treats Hawking radiation as a tunneling process in a spherically symmetric spacetime, is extended to the stationary axisymmetric Kerr spacetime. A generalized Painleve coordinate system (Painleve–Kerr coordinates) is introduced. The new coordinates are well-behaved at the event horizon. Constant-time slices are just flat Euclidean space in radial and satisfy Landau's condition of clock synchronization. The tunneling process across the Kerr black hole event horizon is investigated and the correctd radiation spectrum is obtained. The result is consistent with an underlying unitary theory.

In this paper, we first rewrite the Lagrangian density of the electromagnetic field corresponding to the source with electric and magnetic charges. Then, in the background of Reissner–Nordström black hole spacetime, we extend the Parikh–Wilczek tunneling framework and calculate the emission spectrum of the outgoing particles with electric and magnetic charges. For the sake of simplicity, we only consider the case that the rate of electric and magnetic charge of the emission particle is constant and equals that of the black hole. In this case, the emission spectrum deviates from the pure thermal spectrum, but it is consistent with an underlying unitary theory and takes the same functional form as that of the uncharged massless particles. Finally, a discussion about the result is presented.

Hawking radiation viewed as a semiclassical tunneling process of particles from the event horizon of general static black holes is investigated by taking the back-reaction of the emitted particles into account. In a general static spacetime, the emission rates of massless, massive and massive charged particles are computed respectively and the tunneling probabilities are obtained. Our results show that when energy and charge conservation are incorporated into the radiation process, the emission rate of the tunneling particles is related to changes of the Bekenstein-Hawking entropies of the black hole before and after the emission, thus it is consistent with an underlying unitary theory. The present results are obtained in a general way, no matter what the special static metric function is, and hence a generalization for the results found in the literature is given. Some remarks on the tunneling method are presented.

It has recently been claimed that Zitterbewegung has been observed. However, we argue that it is not an observable and that the authors' observations must be reinterpreted.

We analyze the (discrete) spectrum of the semirelativistic "spinless-Salpeter" Hamiltonian

In this contribution I will present a review about bouncing models arriving from quantum cosmology and show how one can describe the evolution of quantum cosmological perturbations on them. I will discuss the important role played by the choice of the precise quantum theory one selects to interpret the wave function of the Universe in order to obtain simple equations for the evolution of quantum perturbations on these quantum cosmological backgrounds. I will present the predictions of these models concerning the power spectrum of cosmological perturbations and how they can be compared with the usual results obtained from inflationary models. Finally, I will present the new implications of these results for quantum theory.

The Euclidean space, obtained by the analytical continuation of time, to an imaginary time, is used to model thermal systems. In this work, it is taken a step further to systems with spatial thermal variation, by developing an equivalence between the spatial variation of temperature in a thermal bath and the curvature of the Euclidean space. The variation in temperature is recast as a variation in the metric, leading to a curved Euclidean space. The equivalence is substantiated by analyzing the Polyakov loop, the partition function and the periodicity of the correlation function. The bulk thermodynamic properties like the energy, entropy and the Helmholtz free energy are calculated from the partition function, for small metric perturbations, for a neutral scalar field. The Dirac equation for an external Dirac spinor, traversing a thermal bath with spatial thermal gradients, is solved in the curved Euclidean space. The fundamental behavior exhibited by the Dirac spinor eigenstate, may provide a possible mechanism to validate the theory, at a more basal level, than examining only bulk thermodynamic properties. Furthermore, in order to verify the equivalence at the level of classical mechanics, the geodesic equation is analyzed in a classical backdrop. The mathematical apparatus is borrowed from the physics of quantum theory in a gravity-induced space–time curvature. As spatial thermal variations are obtainable at quantum chromodynamic or quantum electrodynamic energies, it may be feasible for the proposed formulation to be validated experimentally.

Cold dark matter (DM) is conceived as a gas of massive particles that undergo collisions, interact gravitationally and exchange quanta of energy. A new nonrelativistic quantum theory is presented for this model of DM, based on a recently discovered equation for a spinless, no charge and free particle. This theory describes the quantum processes undergoing by the particles, specifies the required characteristic wavelength of the quanta of energy, gives constraints on the mass of DM particles, and predicts a detectable gravitational wave background associated with DM halos.

The proton conductivity and thermodynamic features, arising from motions of the ionic and bonded defects, in hydrogen-bonded molecular systems have been investigated by the quantum-mechanical method and the transfer integral way in our model, in which the collective effect and the mutual correlation between the protonic and heavy ionic sublattices are specially considered. We first derived the equations of motion and its soliton solutions from the model Hamiltonian. The results obtained show that this model can simultaneously support motions of the ionic and bonded defects which are due to competition of the double-well potential and non-linearly coupled interaction between the protons and heavy ions. Thus we find out the mobility of the kink-antikink pair and electrical-conductivity of the proton transfer in the hydrogen-bonded systems exposed in an externally applied electrical-field through the dynamic equation of the kink-antikink pair and its solution in this model. For ice, the mobility and electrical conductivity of the proton transfer obtained are about (6.5 - 6.9)×10^-6m²/V · s and (7.6 - 8.1)×10^-3(Ω · m)^-1, respectively, which are in the domain of semiconductors and are basically consistent with experimental values for the crystal. Finally we calculate the free energy and specific heat of the systems with finite temperature by the model Hamiltonian and transfer integral way. The specific heat is also consistent with experimental data. This is a very interesting result.

We discuss the motivation and main results of a quantum theory over a Galois field (GFQT). The goal of the paper is to describe main ideas of GFQT in a simplest possible way and to give clear and simple arguments that GFQT is a more natural quantum theory than the standard one.

Quantum control strategy is discussed from the perspective of quantum information. First, the constraints imposed on quantum control by quantum theory are analyzed. Then some quantum control schemes based on quantum information are discussed, such as teleportation-based distant quantum control, quantum feedback control using quantum cloning and state recognition, quantum control based on measurement and Grover iteration. Finally, some applications of quantum control theory in quantum information and quantum computation such as quantum error correction coding, universality analysis of quantum computation, feedback-induced entanglement enhancement, etc., are presented and the potential applications of quantum control are also prospected.

A generalization of quantum mechanics is proposed, where the Lagrangian is the general form. The new quantum wave equation can describe the particle which is in general potential , and the Schrödinger equation is only suited for the particle in common potential V(r, t). We think these new quantum wave equations can be used in some fields.

We develop a quantum theory to deal with the coherent magnon excitation in monolayer magnetic nanodots induced by a circularly polarized light. In our theoretical model, the exchange interaction, the magnetic dipole interaction and the light-matter interaction are all taken into account and an effective dynamic equations governing the magnon excitation is derived by a continuum approximation. Our theoretical model shows that the helicity of light and the magnetic dipole interaction govern the magnon excitation and result in the occurrence of various patterns for the spin z-component distribution. We present a scheme to manipulate the single-mode magnon excitation by properly tuning the light frequency.

In the present note, we consider the annihilation and creation operators with complex friction coefficient and we find the coherent, squeezed states, the uncertainty Heisenberg relation and the behavior of the PT and, CPT symmetries. Also we demonstrated that the (CK) Hamiltonian is a special case of the complex time-dependent mass.

The approach to question answering is challenging because it usually requires finding useful information from within and between question and answer sentences for sentence semantic matching. The key information mined from existing question and answer sentences, as a supplement to semantic information, maybe helpful for this task. However, capturing the intra-sentence and inter-sentence semantic interactions is somewhat difficult given the implicit interrelationships between question and answer sentences. Although the learning effect of multi-layer neural network is good, it lacks explanatory and theoretical support. This paper mainly studies how to select the best answer sentence from a set of question and answer sentences, mine information more effectively, perform semantic matching, and have a certain interpretability. Therefore, we propose a hierarchical attention network (QHAN) based on the mathematical framework of quantum theory, which integrates the attention mechanism under quantum measurement and density matrix (DMATT) and the attention mechanism under quantum weak measurement and weak value (WMATT) in one in a unified model framework. QHAN can not only discover key sentences in a set of question and answer sentences and key words in a sentence, but also perform sentence semantic matching quickly and accurately. Furthermore, QHAN has the advantage of interpretability in terms of models due to the physical meaning and attentional full weight distribution implied by quantum theory. Extensive experiments on the question answering dataset show that our method is comparable to the baselines and can explain why the selected question and answer sentence is the best option in terms of intra-sentence and inter-sentence attention distributions.