A classical hamiltonian method for calculating IR-Resonant photodesorption rates

Summary In this work, classical nonlinear dynamical methods are used to study photodesorption induced by IR-laser resonant excitation of an internal vibrational mode of a physisorbed molecule. Starting from the large disagreement between the experimental values of the photodesorption rates and the theoretical quantum perturbative ones for CH₃F/NaCl, the Elastic-Resonant-State Decay (ERSD) model is analysed focusing attention on the nonexponential time decay behaviour of the survival probability of the system, that shows two different time scales. This is obtained by a suitable average of classical trajectories calculated by integrating Hamilton’s equations of motion. The Poincaré sections are used to clarify the details of the microscopic dynamics of the IR-photodesorption, pointing out the dynamical role of cantori as responsible for desorption occurring on a longer time scale. A method to build up the separatrix for the ERSD system is proposed, stressing that such a separatrix acts as a bottleneck against the energy flux exchanged between the physisorption and the intramolecular bond of the adsorbate. A calculation of the photodesorption rate when a condition of fast relaxation between the two bonds is verified, is performed using the Transport Theory in Hamiltonian System. The values of the photodesorption rate obtained by this approach are in good agreement with those obtained by integrating numerically the equations of motion.     

Extracting dynamical equations from experimental data is NP hard

The behavior of any physical system is governed by its underlying dynamical equations. Much of physics is concerned with discovering these dynamical equations and understanding their consequences. In this Letter, we show that, remarkably, identifying the underlying dynamical equation from any amount of experimental data, however precise, is a provably computationally hard problem (it is NP hard), both for classical and quantum mechanical systems. As a by-product of this work, we give complexity-theoretic answers to both the quantum and classical embedding problems, two long-standing open problems in mathematics (the classical problem, in particular, dating back over 70?years).     

Group Foundations of Quantum and Classical Dynamics : Towards a Globalization and Classification of Some of Their Structures

This paper is devoted to a constructiveand critical analysis of the structure of certain dynamical systems from a group manifold point of view recently developed. This approach is especially suitable for discussing the structure of the quantum theory, the classical limit, the Hamilton-Jacobi theory and other problems such as the definition and globalization of the Poincaré-Cartan form which appears in the variational approach to higher order dynamical systems. At the same time, i t opens a way for the classification of all hamiltonian and lagrangian systems associated with suitably defined dynamical groups. Both classical and quantum dynamics are discussed, and examples of all the different structures appearingin the theory are provided, including a treatment of constrained and generalized higher order dynamical systems.     

Classically induced suppression of energy growth in a chaotic quantum system

Recent experiments with Bose–Einstein condensates (BEC) in traps and speckle potentials have explored the dynamical regime in which the evolving BEC clouds localize due to the influence of classical dynamics. The growth of their mean energy is effectively arrested. This is in contrast with the well-known localization phenomena that originate due to quantum interferences. We show that classically induced localization can also be obtained in a classically chaotic, non-interacting system. In this work, we study the classical and quantum dynamics of non-interacting particles in a double-barrier structure. This is essentially a non-KAM system and, depending on the parameters, can display chaotic dynamics inside the finite well between the barriers. However, for the same set of parameters, it can display nearly regular dynamics above the barriers. We exploit this combination of two qualitatively different classical dynamical features to obtain saturation of energy growth. In the semiclassical regime, this classical mechanism strongly influences the quantum behaviour of the system.     

Higher Order Quantum Onsager Coefficients from Dynamical Invariants

Functionals representing dynamical invariants under unitary quantum dynamics of open systems are used to derive Onsager coefficients for entropy production in irreversible processes if the nonunitary time evolution is determined by quantum dynamical semigroups. The procedure allows a derivation from first principles of the quantum analogue to the classical case.     

Time dependence in quantum mechanics

It is shown that the time-dependent equations (Schr?dinger and Dirac) for a quantum system can be derived from the time-independent equation for the larger object of the system interacting with its environment, in the limit that the dynamical variables of the environment can be treated semiclassically. The time which describes the quantum evolution is then provided parametrically by the classical evolution of the environment variables. The method used is a generalization of that known for a long time in the field of ion-atom collisions, where it appears as a transition from the full quantum mechanical perturbed stationary states to the impact parameter method in which the projectile ion beam is treated classically. Received 25 October 1999     

Revisiting Consistency Conditions for Quantum States of Systems on Closed Timelike Curves: An Epistemic Perspective

There has been considerable recent interest in the consequences of closed timelike curves (CTCs) for the dynamics of quantum mechanical systems. A vast majority of research into this area makes use of the dynamical equations developed by Deutsch, which were developed from a consistency condition that assumes that mixed quantum states uniquely describe the physical state of a system. We criticize this choice of consistency condition from an epistemic perspective, i.e., a perspective in which the quantum state represents a state of knowledge about a system. We demonstrate that directly applying Deutsch’s condition when mixed states are treated as representing an observer’s knowledge of a system can conceal time travel paradoxes from the observer, rather than resolving them. To shed further light on the appropriate dynamics for quantum systems traversing CTCs, we make use of a toy epistemic theory with a strictly classical ontology due to Spekkens and show that, in contrast to the results of Deutsch, many of the traditional paradoxical effects of time travel are present.     

Stability of quantum spins in a magnetic field

Continuous representations of the dynamical group, and the corresponding generalized coherent states, are used to conjugate dynamics of a system of quantum spins to that of a classical Hamiltonian system. Stability of the Hamiltonian system obtained are studied, using linear stability analyses and results from the perturbation theory. Quantum evolution of any of the compound‐spins components is described exactly by classical Hamilton's equations. No semiclassical asymptotics in the analyses or explicit time‐dependence has been involved.     

Dynamics of vibrational chaos and entanglement in triatomic molecules： Lie algebraic model

In this paper, the dynamics of chaos and the entanglement in triatomic molecular vibrations are investigated. On the classical aspect, we study the chaotic trajectories in the phase space. We employ the linear entropy to examine the dynamical entanglement of the two bonds on the quantum aspect. The correspondence between the classical chaos and the quantum dynamical entanglement is also investigated. As an example, we apply our algebraic model to molecule H2O.     

Quantum semi-Markov processes

We construct a large class of non-Markovian master equations that describe the dynamics of open quantum systems featuring strong memory effects, which relies on a quantum generalization of the concept of classical semi-Markov processes. General conditions for the complete positivity of the corresponding quantum dynamical maps are formulated. The resulting non-Markovian quantum processes allow the treatment of a variety of physical systems, as is illustrated by means of various examples and applications, including quantum optical systems and models of quantum transport.     

Classical and quantum chaos in atom optics

The interaction of an atom with an electro-magnetic field is discussed in the presence of a time periodic external modulating force. It is explained that a control on atom by electro-magnetic fields helps to design the quantum analog of classical optical systems. In these atom optical systems chaos may appear at the onset of external fields. The classical and quantum chaotic dynamics is discussed, in particular in an atom optics Fermi accelerator. It is found that the quantum dynamics exhibits dynamical localization and quantum recurrences.     

Dynamics and entanglement of a membrane-in-the-middle optomechanical system in the extremely-large-amplitude regime

The study of optomechanical systems has attracted much attention, most of which are concentrated in the physics in the smallamplitude regime. While in this article, we focus on optomechanics in the extremely-large-amplitude regime and consider both classical and quantum dynamics. Firstly, we study classical dynamics in a membrane-in-the-middle optomechanical system in which a partially reflecting and flexible membrane is suspended inside an optical cavity. We show that the membrane can present self-sustained oscillations with limit cycles in the shape of sawtooth-edged ellipses and exhibit dynamical multistability. Then, we study the dynamics of the quantum fluctuations around the classical orbits. By using the logarithmic negativity, we calculate the evolution of the quantum entanglement between the optical cavity mode and the membrane during the mechanical oscillation. We show that there is some synchronism between the classical dynamical process and the evolution of the quantum entanglement.     

SU(3) Local Gauge Field Theory as Effective Dynamics of Composite Gluons

The effective dynamics of quarks is described by a nonperturbatively regularized NJL model equation with canonical quantization and probability interpretation. The quantum theory of this model is formulated in functional space and the gluons are considered as relativistic bound states of colored quark-antiquark pairs. Their wave functions are calculated as eigenstates of hardcore equations, and their effective dynamics is derived by weak mapping in functional space. This leads to the phenomenological SU(3) gauge invariant gluon equations in functional formulation, i.e., the local gauge symmetry is a dynamical effect resulting from the dynamics of the quark model.     

Back-reaction equations for isotropic cosmologies when nonconformal particles are created

A model proposed some years ago by Hartle to study the back reaction in a cosmological model due to the creation of massless non-conformally coupled particles is reexamined. The model consists of a spatially flat FRW spacetime with a classical source made of two perfect fluids one a radiative fluid and the other a baryonic fluid with the equation of state of dust, and it is assumed that the ratio of baryons to photons is small. The back-reaction equations for the cosmological scale factor are derived using a CTP (closed time path) effective action method. Making use of the connection, in the semiclassical context, between the CTP effective action and the influence functional in quantum statistical mechanics, improved back-reaction equations are derived which take into account the fluctuations of the stress-energy tensor of the quantum field. These new dynamical equations are real and causal and predict stochastic fluctuations for the cosmological scale factor.     

Dynamical renormalization group approach to relaxation in quantum field theory

The real time evolution and relaxation of expectation values of quantum fields and of quantum states are computed as initial value problems by implementing the dynamical renormalization group (DRG). Linear response is invoked to set up the renormalized initial value problem to study the dynamics of the expectation value of quantum fields. The perturbative solution of the equations of motion for the field expectation values of quantum fields as well as the evolution of quantum states features secular terms, namely terms that grow in time and invalidate the perturbative expansion for late times. The DRG provides a consistent framework to resum these secular terms and yields a uniform asymptotic expansion at long times. Several relevant cases are studied in detail, including those of threshold infrared divergences which appear in gauge theories at finite temperature and lead to anomalous relaxation. In these cases the DRG is shown to provide a resummation akin to Bloch-Nordsieck but directly in real time and that goes beyond the scope of Bloch-Nordsieck and Dyson resummations. The nature of the resummation program is discussed in several examples. The DRG provides a framework that is consistent, systematic, and easy to implement to study the non-equilibrium relaxational dynamics directly in real time that does not rely on the concept of quasiparticle widths.     

Zeno dynamics for open quantum systems

In this paper, we formulate limit Zeno dynamics of general open systems as the adiabatic elimination of fast components. We are able to exploit previous work on adiabatic elimination of quantum stochastic models to give explicitly the conditions under which open Zeno dynamics will exist. The open systems formulation is further developed as a framework for Zeno master equations, and Zeno filtering (that is, quantum trajectories based on a limit Zeno dynamical model). We discuss several models from the point of view of quantum control. For the case of linear quantum stochastic systems, we present a condition for stability of the asymptotic Zeno dynamics.     

Prequantum Classical Statistical Field Theory: Schrödinger Dynamics of Entangled Systems as a Classical Stochastic Process

The idea that quantum randomness can be reduced to randomness of classical fields (fluctuating at time and space scales which are essentially finer than scales approachable in modern quantum experiments) is rather old. Various models have been proposed, e.g., stochastic electrodynamics or the semiclassical model. Recently a new model, so called prequantum classical statistical field theory (PCSFT), was developed. By this model a “quantum system” is just a label for (so to say “prequantum”) classical random field. Quantum averages can be represented as classical field averages. Correlations between observables on subsystems of a composite system can be as well represented as classical correlations. In particular, it can be done for entangled systems. Creation of such classical field representation demystifies quantum entanglement. In this paper we show that quantum dynamics (given by Schrödinger’s equation) of entangled systems can be represented as the stochastic dynamics of classical random fields. The “effect of entanglement” is produced by classical correlations which were present at the initial moment of time, cf. views of Albert Einstein.