Quantum-mechanical tunneling in associative neural networks

We investigate the quantum-mechanical tunneling between the “patterns" of the, so-called, associative neural networks. Being the relatively stable minima of the “configuration-energy" space of the networks, the “patterns" represent the macroscopically distinguishable states of the neural nets. Therefore, the tunneling represents a macroscopic quantum effect, but with some special characteristics. Particularly, we investigate the tunneling between the minima of approximately equal depth, thus requiring no energy exchange. If there are at least a few such minima, the tunneling represents a sort of the “random walk" process, which implies the quantum fluctuations in the system, and therefore “malfunctioning" in the information processing of the nets. Due to the finite number of the minima, the “random walk" reduces to a dynamics modeled by the, so-called, Pauli master equation. With some plausible assumptions, the set(s) of the Pauli master equations can be analytically solved. This way comes the main result of this paper: the quantum fluctuations due to the quantum-mechanical tunneling can be “minimized" if the “pattern"-formation is such that there are mutually “distant" groups of the “patterns", thus providing the “zone" structure of the “pattern" formation. This qualitative result can be considered as a basis of the efficient deterministic functioning of the associative neural nets. Received 15 July 1999     

Consistent Histories in Quantum Cosmology

We illustrate the crucial role played by decoherence (consistency of quantum histories) in extracting consistent quantum probabilities for alternative histories in quantum cosmology. Specifically, within a Wheeler-DeWitt quantization of a flat Friedmann-Robertson-Walker cosmological model sourced with a free massless scalar field, we calculate the probability that the universe is singular in the sense that it assumes zero volume. Classical solutions of this model are a disjoint set of expanding and contracting singular branches. A naive assessment of the behavior of quantum states which are superpositions of expanding and contracting universes suggests that a “quantum bounce” is possible i.e. that the wave function of the universe may remain peaked on a non-singular classical solution throughout its history. However, a more careful consistent histories analysis shows that for arbitrary states in the physical Hilbert space the probability of this Wheeler-DeWitt quantum universe encountering the big bang/crunch singularity is equal to unity. A quantum Wheeler-DeWitt universe is inevitably singular, and a “quantum bounce” is thus not possible in these models.     

Quantum decoherence in the theory of open systems

Within the framework of the Lindblad theory for open quantum systems, we determine the degree of quantum decoherence of a harmonic oscillator interacting with a thermal bath. It is found that the system manifests a quantum decoherence which is more and more significant in time. We also calculate the decoherence time scale and analyze the transition from quantum to classical behavior of the considered system. The text was submitted by the author in English.     

Relativistic quantum events

Standard quantum theory is inadequate to explain the mechanisms by which potential becomes actual. It is inadequate and therefore unable to describe generation of events. Niels Bohr emphasized long ago that the classical part of the world is necessary. John Bell stressed the same point: that measurement≓ cannot even be defined within the standard quantum theory, and he sought a solution within hidden variable theories and his concept of beables.≓ Today it is customary to try to explain emergence of the classical world through a decoherence mechanism due to environment.≓ But, we believe, as it was with the concept of measurement, environment≓ itself cannot be defined within the standard quantum theory. We have proposed a semiphenomenological solution to this problem by introducing explicitly, from the very beginning, classical degrees of freedom, and by coupling these degrees of freedom, through a Lindblad type coupling, to the quantum world. The resulting theory, we call event-enhanced quantum theory.≓ EEQT allows us to describe an event-generating mechanism for individual quantum systems under continuous observation. The objections of John Bell are met and precise definitions of an experiment≓ and of a measurement≓ have been given within EEQT. However EEQT is, essentially, a nonrelativistic theory. In the present paper we extend the ideas of L. P. Horwitz and C. Piron and we propose a relativistic version of EEQT, with an event-generating algorithm for spin one-half particle detectors. The algorithm is based on proper time formulation of the relalivistic quantum theory. Although we use indefinite metric, all the probabilities controlling the random process of the detector clicks are nonnegative.     

Ajellium model analysis on quantum growth of metal nanowiresand nanomesas

A simple jellium model is used to investigate the stability of a metal nanowire as a function of its size. The theoretical results from the model indicate the quantum selectivity of preferable radii of nanowires, in apparent agreement with the experimental observations. It is consequently suggested that a series of stable “magic numbers” and “instability gaps” observed in the synthesis experiments of Au nanowires is mainly attributed to the quantum-mechanical behavior. These stable radii can be achieved by rearranging atoms during the formation of nanowires. The model is also used to analyze the growth of Au nanomesas on a graphite surface, and the puzzling growth behavior of Au nanomesas can be reasonably explained.      

A Simple Example of “Quantum Darwinism”: Redundant Information Storage in Many-Spin Environments

As quantum information science approaches the goal of constructing quantum computers, understanding loss of information through decoherence becomes increasingly important. The information about a system that can be obtained from its environment can facilitate quantum control and error correction. Moreover, observers gain most of their information indirectly, by monitoring (primarily photon) environments of the “objects of interest.” Exactly how this information is inscribed in the environment is essential for the emergence of “the classical” from the quantum substrate. In this paper, we examine how many-qubit (or many-spin) environments can store information about a single system. The information lost to the environment can be stored redundantly, or it can be encoded in entangled modes of the environment. We go on to show that randomly chosen states of the environment almost always encode the information so that an observer must capture a majority of the environment to deduce the system’s state. Conversely, in the states produced by a typical decoherence process, information about a particular observable of the system is stored redundantly. This selective proliferation of “the fittest information” (known as Quantum Darwinism) plays a key role in choosing the preferred, effectively classical observables of macroscopic systems. The developing appreciation that the environment functions not just as a garbage dump, but as a communication channel, is extending our understanding of the environment’s role in the quantum-classical transition beyond the traditional paradigm of decoherence.     

Particles and events in classical off-shell electrodynamics

Despite the many successes of the relativistic quantum theory developed by Horwitz et al., certain difficulties persist in the associated covariant classical mechanics. In this paper, we explore these difficulties through an examination of the classical. Coulomb problem in the framework of off-shell electrodynamics. As the local gauge theory of a covariant quantum mechanics with evolution paratmeter τ, off-shell electrodynamics constitutes a dynamical theory of ppacetime events, interacting through five τ-dependent pre-Maxwell potentials. We present a straightforward solution of the classical equations of motion, for a test event traversing the field induced by a “fixed” event (an event moving uniformly along the time axis at a fixed point in space). This solution is seen to be unsatisfactory, and reveals the essential difficulties in the formalism at the classical levels. We then offer a new model of the particle current—as a certain distribution of the event currents on the worldline—which eliminates these difficulties and permits comparison of classisical off-shell electrodynamics with the standard Maxwell theory. In this model, the “fixed” event induces a Yukawa-type potential, permitting a semiclassical identification of the pre-Maxwell time scale λ with the inverse mass of the intervening photon. Numerical solutions to the equations of motion are compared with the standard Maxwell solutions, and are seen to coincide when λ≳10⁻⁶ seconds, providing an initial estimate of this parameter. It is also demonstrated that the proposed model provides a natural interpretation for the photon mass cut-off required for the renormalizability of the off-shell quantum electrodynamics.     

Decoherence within a single atom

An “almost diagonal” reduced density matrix (in coordinate representation) is usually a result of environment induced decherence and is considered the sign of classical behavior. We show that the proton of a ground state hydrogen atom can indeed possess such a density matrix. This example demonstrates that the “almost diagonal” structure may be derived from an interaction with a low number of degrees of freedom which play the role of the environment. We also show that decoherence effects in our example can only be observed if the interaction with the measuring device is significantly faster than the interaction with the environment (the electron). In the opposite case, when the interaction with the environment is significant during the measurement process, coherence is maintained. Finally, we propose a neutron scattering experiment on cold He atoms to observe decoherence which shows up as an additional positive contribution to the differential scattering cross section. This contribution is inversely proportional to the bombarding energy.     

Persistent current in metals with a large dephasing rate

In a weakly disordered metal electron interactions are responsible for both decoherence of the quasi-particles as well as for quantum corrections to thermodynamic properties. We consider electrons which are interacting with two-level-systems. We show that the two-level-systems enhance the average equilibrium (“persistent”) current in an ensemble of mesoscopic rings. The result supports the recent suggestion that two puzzles in mesoscopic physics may be related: The low temperature saturation of the dephasing time and the high persistent current in rings. Received 26 May 2000     

Quantum to classical transition for random walks

We look at two possible routes to classical behavior for the discrete quantum random walk on the integers: decoherence in the quantum "coin" which drives the walk, or the use of higher-dimensional (or multiple) coins to dilute the effects of interference. We use the position variance as an indicator of classical behavior and find analytical expressions for this in the long-time limit; we see that the multicoin walk retains the "quantum" quadratic growth of the variance except in the limit of a new coin for every step, while the walk with decoherence exhibits "classical" linear growth of the variance even for weak decoherence.     

Quantum decoherence from adiabatic entanglement with external one or a few degrees of freedom

Based on the Born-Oppenhemer approximation, the concept of adiabatic quantum entanglement is introduced to account for quantum decoherence of a quantum system due to its interaction with a large system of one or a few degrees of freedom. In the adiabatic limit, it is shown that the wave function of the total system formed by the quantum system plus the large system can be factorized as an entangled state with correlation between adiabatic quantum states and quasi-classical motion configurations of the large system. In association with a novel viewpoint about quantum measurement, which has been directly verified by most recent experiments [e.g., S. Durr et al., Nature 33, 359 (1998)], it is shown that the adiabatic entanglement is indeed responsible for the quantum decoherence and thus can be regarded as a “clean” quantum measurement when the large system behaves as a classical object. By taking the large system respectively to be a macroscopically distinguishable spatial variable, a high spin system and a harmonic oscillator with a coherent initial state, three illustrations are presented with their explicit solutions in this paper. Received 26 February 2000 and Received in final form 14 July 2000     

Quantum Lyapunov Exponents

We show that it is possible to associate univocally with each given solution of the time-dependent Schrödinger equation a particular phase flow (quantum flow) of a non-autonomous dynamical system. This fact allows us to introduce a definition of chaos in quantum dynamics (quantum chaos), which is based on the classical theory of chaos in dynamical systems. In such a way we can introduce quantities which may be appelled quantum Lyapunov exponents. Our approach applies to a non-relativistic quantum-mechanical system of n charged particles; in the present work numerical calculations are performed only for the hydrogen atom. In the computation of the trajectories we first neglect the spin contribution to chaos, then we consider the spin effects in quantum chaos. We show how the quantum Lyapunov exponents can be evaluated and give several numerical results which describe some properties found in the present approach. Although the system is very simple and the classical counterpart is regular, the most non-stationary solutions of the corresponding Schrödinger equation are chaotic according to our definition.     

Quantum Algorithms Know in Advance 50% of the Solution They Will Find in the Future

Quantum algorithms require less operations than classical algorithms. The exact reason of this has not been pinpointed until now. Our explanation is that quantum algorithms know in advance 50% of the solution of the problem they will find in the future. In fact they can be represented as the sum of all the possible histories of a respective “advanced information classical algorithm”. This algorithm, given the advanced information (50% of the bits encoding the problem solution), performs the operations (oracle’s queries) still required to identify the solution. Each history corresponds to a possible way of getting the advanced information and a possible result of computing the missing information. This explanation of the quantum speed up has an immediate practical consequence: the speed up comes from comparing two classical algorithms, with and without advanced information, with no physics involved. This simplification could open the way to a systematic exploration of the possibilities of speed up.     

Multiple-beam Ramsey interference and quantum decoherence

We study the effect of photon scattering from a path of a four-beam atomic interference setup, which is based on a cesium atomic beam and two subsequent optical Ramsey pulses projecting the atoms onto a multilevel dark state. While in two-beam interference, any attempt to keep track of an interfering path reduces the fringe contrast, we demonstrate that photon scattering in a multiple-path arrangement cannot only lead to a decrease, but - under certain conditions - also to an increase of the interference contrast. The results are confirmed by a density-matrix calculation. We are aware that in all cases the “which-path” information carried away by the scattered photons leads to a loss of information that is contained in the atomic quantum state. An approach to quantify this “which-path” information using observed fringe signals is presented; it allows for an appropriate measure of quantum decoherence in multiple-path interference. Received: 27 July 2000 / Published online: 6 December 2000     

What is “System”: Some Decoherence-Theory Arguments

We discuss the possibility of making the initial definitions of mutually different (possibly interacting, or even entangled) systems in the context of decoherence theory. We point out relativity of the concept of elementary physical system as well as point out complementarity of the different possible divisions of a composite system into “subsystems,” thus eventually sharpening the issue of “what is system.”     

Quantum One Go Computation and the Physical Computation Level of Biological Information Processing

By extending the representation of quantum algorithms to problem-solution interdependence, the unitary evolution part of the algorithm entangles the register containing the problem with the register containing the solution. Entanglement becomes correlation, or mutual causality, between the two measurement outcomes: the string of bits encoding the problem and that encoding the solution. In former work, we showed that this is equivalent to the algorithm knowing in advance 50% of the bits of the solution it will find in the future, which explains the quantum speed up. Mutual causality between bits of information is also equivalent to seeing quantum measurement as a many body interaction between the parts of a perfect classical machine whose normalized coordinates represent the qubit populations. This “hidden machine” represents the problem to be solved. The many body interaction (measurement) satisfies all the constraints of a nonlinear Boolean network “together and at the same time”—in one go—thus producing the solution.