Spontaneous emission of the non-Wiener type

The spontaneous emission of a quantum particle and superradiation of an ensemble of identical quantum particles in a vacuum electromagnetic field with zero photon density are examined under the conditions of significant Stark particle and field interaction. New fundamental effects are established: suppression of spontaneous emission by the Stark interaction, an additional “decay” shift in energy of the decaying level as a consequence of Stark interaction unrelated to the Lamb and Stark level shifts, excitation conservation phenomena in a sufficiently dense ensemble of identical particles and suppression of superradiaton in the decay of an ensemble of excited quantum particles of a certain density. The main equations describing the emission processes under conditions of significant Stark interaction are obtained in the effective Hamiltonian representation of quantum stochastic differential equations. It is proved that the Stark interaction between a single quantum particle and a broadband electromagnetic field is represented as a quantum Poisson process and the stochastic differential equations are of the non-Wiener (generalized Langevin) type. From the examined case of spontaneous emission of a quantum particle, the main rules are formulated for studying open systems in the effective Hamiltonian representation.     

Spreading of atomic wave packets and semiclassical chaos

The correspondence between the statistical properties of the evolution of a quantum system and Lyapunov instability and the chaos of its semiclassical analog has been demonstrated. The results of the analyses of atomic motion in a laser field in the semiclassical approximation (dynamics is described by several nonlinear equations) and without this approximation (dynamics is described by an infinite system of linear equations) are compared. In the ranges of the parameters for which the semiclassical dynamics of point-like atoms is unstable, the fast “spreading” of quantized wave packets in the momentum space is observed. Thus, deterministic chaos “imitates” the statistics of the quantum nondeterministic effects, although the semiclassical and quantum solutions are fundamentally different.     

Effective Dynamics for Particles Coupled to a Quantized Scalar Field

We consider a system of N non-relativistic spinless quantum particles (“electrons”) interacting with a quantized scalar Bose field (whose excitations we call “photons”). We examine the case when the velocity v of the electrons is small with respect to the one of the photons, denoted by c (v/c = ε ≪ 1). We show that dressed particle states exist (particles surrounded by “virtual photons”), which, up to terms of order (v/c)³, follow Hamiltonian dynamics. The effective N-particle Hamiltonian contains the kinetic energies of the particles and Coulomb-like pair potentials at order (v/c)⁰ and the velocity dependent Darwin interaction and a mass renormalization at order (v/c)². Beyond that order the effective dynamics are expected to be dissipative. The main mathematical tool we use is adiabatic perturbation theory. However, in the present case there is no eigenvalue which is separated by a gap from the rest of the spectrum, but its role is taken by the bottom of the absolutely continuous spectrum, which is not an eigenvalue. Nevertheless we construct approximate dressed electron subspaces, which are adiabatically invariant for the dynamics up to order . We also give an explicit expression for the non-adiabatic transitions corresponding to emission of free photons. For the radiated energy we obtain the quantum analogue of the Larmor formula of classical electrodynamics.     

Consequences of a Cosmological Phase Transition at the TeV Scale

A finite vacuum energy density implies the existence of a UV scale for gravitational modes. This gives a phenomenological scale to the dynamical equations governing the cosmological expansion that must satisfy constraints consistent with quantum measurability and spatial flatness. Examination of these constraints for the observed dark energy density establishes a time interval from the transition to the present, suggesting major modifications from the thermal equations of state far from Planck density scales. The assumption that a phase transition initiates the radiation dominated epoch is shown under several scenarios to be able to produce fluctuations to the CMB of the order observed. Quantum measurability constraints (eg. uncertainly relations) define cosmological scales bounded by luminal expansion rates. It is shown that the dark energy can consistently be interpreted as being due to the vacuum energy of collective gravitational modes which manifest as the zero-point motions of coherent Planck scale mass units prior to the UV scale onset of gravitational quantum de-coherence for the cosmology. A cosmological model with multiple scales, one of which replaces an apparent cosmological “constant”, is shown to reproduce standard cosmology during intermediate times, while making the exploration of the early and late time cosmology more accessible. Talk presented at the 2006 biennial conference of the International Association for Relativistic Dynamics, June 12–14, University of Connecticut (Storrs).     

Nonrelativistic Quantum Mechanics with Fundamental Environment

Spontaneous transitions between bound states of an atomic system, “Lamb Shift” of energy levels and many other phenomena in real nonrelativistic quantum systems are connected within the influence of the quantum vacuum fluctuations (fundamental environment (FE)) which are impossible to consider in the limits of standard quantum-mechanical approaches. The joint system “quantum system (QS) + FE” is described in the framework of the stochastic differential equation (SDE) of Langevin-Schr?dinger (L-Sch) type, and is defined on the extended space R ³ ⊗ R _{ξ}, where R ³ and R _{ξ} are the Euclidean and functional spaces, respectively. The density matrix for single QS in FE is defined. The entropy of QS entangled with FE is defined and investigated in detail. It is proved that as a result of interaction of QS with environment there arise structures of various topologies which are a new quantum property of the system.     

Reconstruction of the Fermi surface in the pseudogap state of cuprates

Reconstruction of the Fermi surface of high-temperature superconducting cuprates in the pseudogap state is analyzed within a nearly exactly solvable model of the pseudogap state, induced by short-range order fluctuations of the antiferromagnetic (AFM), spin-density wave (SDW), or a similar charge-density wave (CDW) order parameter, competing with the superconductivity. We explicitly demonstrate the evolution from “Fermi arcs” (on the “large” Fermi surface) observed in the ARPES experiments at relatively high temperatures (when both the amplitude and phase of the density waves fluctuate randomly) towards the formation of typical “small” electron and hole “pockets,” which are apparently observed in the de Haas-van Alphen and Hall resistance oscillation experiments at low temperatures (when only the phase of the density waves fluctuate and the correlation length of the short-range order is large enough). A qualitative criterion for the quantum oscillations in high magnetic fields to be observable in the pseudogap state is formulated in terms of the cyclotron frequency, the correlation length of fluctuations, and the Fermi velocity. The text was submitted by the authors in English.     

On the Stability of a Quantum Dynamics of a Bose-Einstein Condensate Trapped in a One-Dimensional Toroidal Geometry

We rigorously analyze the stability of the “quasi-classical” dynamics of a Bose-Einstein condensate with repulsive and attractive interactions, trapped in an effective 1D toroidal geometry. The “classical” dynamics, which corresponds to the Gross-Pitaevskii mean field theory, is stable in the case of repulsive interaction, and unstable (under some conditions) in the case of attractive interaction. The corresponding quantum dynamics for observables is described by using a closed system of linear partial differential equations. In both cases of stable and unstable quasi-classical dynamics the quantum effects represent a singular perturbation to the quasi-classical solutions, and are described by the terms in these equations which consist of a small quasi-classical parameter which multiplies high-order “spatial” derivatives. We demonstrate that as a result of the quantum singularity for observables a convergence of quantum solutions to the corresponding classical solutions exists only for limited times, and estimate the characteristic time-scales of the convergence.     

Variational wave equations of two fermions interacting via scalar,pseudoscalar, vector,pseudovector and tensor fields

We consider a method for deriving relativistic two-body wave equations for fermions in the coordinate representation. The Lagrangian of the theory is reformulated by eliminating the mediating fields by means of covariant Green's functions. Then, the nonlocal interaction terms in the Lagrangian are reduced to local expressions which take into account retardation effects approximately. We construct the Hamiltonian and two-fermion states of the quantized theory, employing an unconventional “empty” vacuum state, and derive relativistic two-fermion wave equations. These equations are a generalization of the Breit equation for systems with scalar, pseudoscalar, vector, pseudovector and tensor coupling.     

Braid Group Statistics Implies Scattering in Three-Dimensional Local Quantum Physics

It is shown that quantum fields for massive particles with braid group statistics (Plektons) in three-dimensional space-time cannot be free, in a quite elementary sense: They must exhibit elastic two-particle scattering into every solid angle, and at every energy. This also implies that for such particles there cannot be any operators localized in wedge regions which create only single particle states from the vacuum and which are well-behaved under the space-time translations (so-called temperate polarization- free generators). These results considerably strengthen an earlier “NoGo-theorem for ’free’ relativistic Anyons”.     

Critical velocity and event horizon in pair-correlated systems with “relativistic” fermionic quasiparticles

The condition for the appearance of an event horizon is considered in pair-correlated systems (superfluids and superconductors) in which the fermionic quasiparticles obey “relativistic” equations. In these systems the Landau critical velocity of superflow corresponds to the speed of light. In conventional systems, such as s-wave superconductors, the superflow remains stable even above the Landau threshold. We show, however, that, in “ relativistic” systems, the quantum vacuum becomes unstable and the superflow collapses after the “speed of light” is reached, so that the horizon cannot appear. Thus an equilibrium dissipationless superflow state and the horizon are incompatible on account of quantum effects. This negative result is consistent with the quantum Hawking radiation from the horizon, which would lead to a dissipation of the flow. Pis’ma Zh. éksp. Teor. Fiz. 67, No. 2, 124–129 (25 January 1998) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Number-Phase Quantization Scheme and the Quantum Effects of a Mesoscopic Electric Circuit at Finite Temperature

For L-C circuit, a new quantized scheme has been proposed in the context of number-phase quantization. In this quantization scheme, the number n of the electric charge q(q=en) is quantized as the charge number operator and the phase difference θ across the capacity is quantized as phase operator. Based on the scheme of number-phase quantization and the thermo field dynamics (TFD), the quantum fluctuations of the charge number and phase difference of a mesoscopic L-C circuit in the thermal vacuum state, the thermal coherent state and the thermal squeezed state have been studied. It is shown that these quantum fluctuations of the charge number and phase difference are related to not only the parameters of circuit, the squeezing parameter, but also the temperature in these quantum states. It is proven that the number-phase quantization scheme is very useful to tackle with quantization of some mesoscopic electric circuits and the quantum effects.     

On the superfluidity of classical liquid in nanotubes,I. Case of even number of neutrons

We show that the superfluidity effect in nanotubes arises in a classical liquid (regarded as the limit as h → 0 of the quantum liquid) and involves not only the Bogolyubov “running waves,” but also a “standing wave.” This is obtained from the variational equations in the context of ultrasecondary quantization. It is stressed that the “atomic” size of the nanotube plays a crucial role in the phenomena.     

Mesoscopic and macroscopic dipole clusters: Structure and phase transitions

A two dimensional (2D) classical system of dipole particles confined by a quadratic potential is studied. This system can be used as a model for rare electrons in semiconductor structures near a metal electrode, indirect excitons in coupled quantum dots etc. For clusters of N ≤ 80 particles ground state configurations and appropriate eigenfrequencies and eigenvectors for the normal modes are found. Monte-Carlo and molecular dynamic methods are used to study the order-disorder transition (the “melting” of clusters). In mesoscopic clusters (N < 37) there is a hierarchy of transitions: at lower temperatures an intershell orientational disordering of pairs of shells takes place; at higher temperatures the intershell diffusion sets in and the shell structure disappears. In “macroscopic” clusters (N > 37) an orientational “melting” of only the outer shell is possible. The most stable clusters (having both maximal lowest nonzero eigenfrequencies and maximal temperatures of total melting) are those of completed crystal shells which are concentric groups of nodes of 2D hexagonal lattice with a number of nodes placed in the center of them. The picture of disordering in clusters is compared with that in an infinite 2D dipole system. The study of the radial diffusion constant, the structure factor, the local minima distribution and other quantities shows that the melting temperature is a nonmonotonic function of the number of particles in the system. The dynamical equilibrium between “solid-like” and “orientationally disordered” forms of clusters is considered.     

Feynman’s Proof of Maxwell Equations: in?the?Context?of Quantum Gravity

Many of us are familiar with Feynman’s “proof” of 1948, as revealed by Dyson, which demonstrates that Maxwell equations of electromagnetism are a consequence of Newton’s laws of motion of classical mechanics and the commutation relations of coordinate and momentum of quantum mechanics. It was Feynman’s purpose to explore the universality of dynamics of particles while making the fewest assumptions. We re-examine this formulation in the context of quantum gravity and show how Feynman’s derivation can be extended to include quantum gravity.     

Glimmers of a Pre-geometric Perspective

Spacetime measurements and gravitational experiments are made by using objects, matter fields or particles and their mutual relationships. As a consequence, any operationally meaningful assertion about spacetime is in fact an assertion about the degrees of freedom of the matter (i.e. non gravitational) fields; those, say for definiteness, of the Standard Model of particle physics. As for any quantum theory, the dynamics of the matter fields can be described in terms of a unitary evolution of a state vector in a Hilbert space. By writing the Hilbert space as a generic tensor product of “subsystems” we analyse the evolution of a state vector on an information theoretical basis and attempt to recover the usual spacetime relations from the information exchanges between these subsystems. We consider generic interacting second quantized models with a finite number of fermionic degrees of freedom and characterize on physical grounds the tensor product structure associated with the class of “localized systems” and therefore with “position”. We find that in the case of free theories no spacetime relation is operationally definable. On the contrary, by applying the same procedure to the simple interacting model of a one-dimensional Heisenberg spin chain we recover the tensor product structure usually associated with “position”. Finally, we discuss the possible role of gravity in this framework.     

A modified Jaynes-Cummings model for an atom interacting with a classical multifrequency field

An open quantum system, which consists of a “dressed” two-level atom, i.e., an atom interacting with a classical multifrequency field, and a single quantized mode of an electromagnetic field, is examined. It is shown that when the frequency of the quantized mode coincides with one of the transition frequencies between the quasienergy levels, two interaction mechanisms, which differ in the dynamics of the populations of the quasienergy states, can be realized. Zh. éksp. Teor. Fiz. 112, 818–827 (September 1997)     

Nucleation kinetics of a solid phase in supercooled melts or liquids under heat-insulating conditions (The Initial Stage)

The initial stage of decomposition of a supercooled melt or a viscous liquid under heat-insulating conditions has been considered in terms of the method of virtual media. The heat removal from the interface is taken as the controlling process in the vicinity of a growing nucleus. In addition to the quasi-steady-state equations (which already became standard) for the nucleation rate and the distribution function of subcritical particles of a new phase, an estimating equation has been derived for the time required to reach steady-state values of these characteristics. Numerical evaluations have been performed for nickel. It has been demonstrated that the chosen model of the controlling process is valid only under the condition of weak heat removal. Attention has been drawn to the difference between the “diffusion” and “thermal” processes of nucleation.     

Quantum effects in cosmological models with singularities

The vacuum expectation values of the energy-momentum tensor of quantized scalar and spinor fields in a de Sitter space of the first kind are calculated. Limiting cases of the obtained exact expressions are considered. It is noted that the de Sitter space is a self-consistent solution of the Einstein equations with allowance for quantum vacuum fluctuations of massless fields.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 67–70, January, 1981.I thank V. M. Mostepanenko and B. N. Sharapov for numerous helpful discussions.     

An embedding for general relativity and its implications for new physics

We show that any solution of the 4D Einstein equations of general relativity in vacuum with a cosmological constant may be embedded in a solution of the 5D Ricci-flat equations with an effective 4D cosmological “constant” Λ that is a specific function of the extra coordinate. For unified theories of the forces in higher dimensions, this has major physical implications. Authors Bahram Mashhoon and Paul Wesson belong to The S.T.M. Consortium, http://astro.uwaterloo.ca/~wesson.     

Vacuum Polarisation Effects in the Lorentz Violating Electrodynamics

In this work we reconsider the one loop calculation for the vacuum polarisation tensor in the Lorentz violating quantum electrodynamics. The electron propagator is “dressed” by a Lorentz breaking extra term in the fermion Lagrangian density. We check gauge invariance and use the Schwinger–Dyson equation to discuss the full photon propagator. After a discussion on a possible photon mass shift, we show how a finite quantum correction can be chosen in a unique way in order to ensure—in the spirit of spontaneously broken theories—the standard normalisation conditions for the vacuum polarisation tensor. Then we comment on possible observable physical consequences on the Lamb-shift.