Long Wave Limit of the Complex Dielectric Function for Coulomb System with Bound States

For plasmas consisting of charged particles an improvement of the RPA dielectric function is considered which accounts especially for the possibility of the formation of bound states. The polarizability contains contributions of bound states as well as of scattering states. The imaginary part of the dielectric function describes optical transitions, and expressions for the electrical conductivity are obtained.     

Hydrodynamic Limit of Brownian Particles Interacting with Short- and Long-Range Forces

We investigate the time evolution of a model system of interacting particles moving in a d-dimensional torus. The microscopic dynamics is first order in time with velocities set equal to the negative gradient of a potential energy term plus independent Brownian motions: is the sum of pair potentials, V(r)+ ^d J(r); the second term has the form of a Kac potential with inverse range . Using diffusive hydrodynamic scaling (spatial scale ^–1, temporal scale ^–2) we obtain, in the limit 0, a diffusive-type integrodifferential equation describing the time evolution of the macroscopic density profile.     

Infrared-Finite Algorithms in QED: The Groundstate of an Atom Interacting with the Quantized Radiation Field

In this paper, the groundstate of a nonrelativistic atom, minimally coupled to the quantized radiation field, and its groundstate energy are constructed by an iteration scheme inspired by [10]. This scheme successively removes an infrared cutoff in momentum space and yields a convergent algorithm enabling us to calculate the groundstate and the groundstate energy, to arbitrary order in the feinstructure constant α ~ 1/137. In forthcoming papers, we will use our result to re-expand the groundstate and, eventually, scattering amplitudes in terms of bare quantities.     

与量子光场相互作用的运动原子的熵压缩

运用量子信息熵理论,研究了与量子光场相互作用的二能级运动原子的熵压缩,讨论了原子运动和场模结构对原子熵压缩的影响,并且比较了分别从基于信息熵测不准关系和海森伯测不准关系出发得出的结果,表明原子的运动导致了原子熵压缩的周期性演化;随着场模结构参量的增大,熵压缩的演化周期缩短,压缩时间延长;选择适当的系统参量,运动原子能够呈现长时间的持续熵压缩效应。当原子反转为零时,基于海伯堡测不准关系的方差压缩定义不再有效,而熵压缩实现了对原子压缩效应的高灵敏量度。     

量子化电磁场中的非经典电子波包:电子与光子的纠缠

文中研究了量子化电磁场中非经典电子波包的运动。当初始光子态是Fock态时,随着电子和光子所组成系统的演化,初台可分离的电子态和光子态会互相纠缠,而且电子几率密度的时间演化呈非经典的分岔和汇合的现象。基到这些非经典特征,电子可以在光子场中被加速和减速,而系统保持能量守恒。     

New Approach for Solving the Lindblad Equation of the Density Operator for a Harmonic Oscillator Interacting with an Electromagnetic Field

By virtue of the thermo entangled state (TES) representation whose one mode is a fictitious one accompanying the system mode, this paper presents a novel approach for deriving density operator for a harmonic oscillator interacting with an electromagnetic field. The Fano factor and the Wigner function in evolution process have been derived.     

Upper and Lower Bound States for Zero Dimensional Space in Scalar Quantum Field Theory

International Journal of Theoretical Physics - The varational method with the Hamiltonian formalism of quantum field theory (QFT) is used to study the bound state for scalar particle and...     

Entanglement Evolution Between Various Subsystems of Two Three-level Atoms Interacting with a Two-mode Quantized Field in the Presence of Converter Terms

In this paper, we study the interaction between two Λ-type three-level atoms (a typical qutrit-qutrit system) and two coupled modes of a quantized radiation field in the presence of field-field interaction (parametric down conversion) which are simultaneously injected within an optical cavity. Then, by applying an appropriate canonical transformation, the introduced model is reduced to a well-known form of the generalized Jaynes-Cummings model. Under particular initial conditions for atoms (in some possible states) and the fields (in the finite dimensional pair coherent state) which may be prepared, the explicit form of the state vector of the whole system is analytically evaluated. In order to find the degree of entanglement between different parts of subsystems (“atom+atom”-field, “atom+field”-atom and atom-atom) the dynamics of entanglement through different measures, namely, linear entropy and negativity is evaluated. In each case, the effect of various types of initial atomic states on the above measures are numerically analyzed, in detail. It is indicated that the amount of entanglement can be tuned by choosing appropriate initial states of atoms. Particularly, it is shown that the entanglement sudden death (ESD) can be controlled by adjusting the initial state of the atoms.     

Dynamical Windings of Random Walks and Exclusion Models. Part I: Thermodynamic Limit in ℤ2

We consider a system consisting of a planar random walk on a square lattice, subjected to stochastic elementary local deformations. Both numerical and theoretical results are reported. Depending on the deformation transition rates, and specifically on a parameter η which breaks the symmetry between the left and right orientation, the winding distribution of the walk is modified, and the system can be in three different phases: folded, stretched and glassy. An explicit mapping is found, leading to consider the system as a coupling of two exclusion processes: particles of the first one move in a landscape defined by particles of the second one, and vice-versa. This can be viewed as an inhomogeneous exclusion process. For all closed or periodic initial sample paths, a convenient scaling permits to show a convergence in law (or almost surely on a modified probability space) to a continuous curve, the equation of which is given by a system of two non linear stochastic differential equations. The deterministic part of this system is explicitly analyzed via elliptic functions. In a similar way, by using a formal fluid limit approach, the dynamics of the system is shown to be equivalent to a system of two coupled Burgers equations.     

Brownian Motion with Restoring Drift: Micro-canonical Ensemble and the Thermodynamic Limit

 We take up the old problem of micro-canonical conditioning in the context of diffusion. Starting with a potential , the Schr?dinger operator with ground state is carried by a conjugation into the diffusion generator with invariant density . The latter motion is made micro-canonical by first conditioning the path to be periodic, , and then further conditioning on the empirical mean-square or ``particle number' . The thermodynamics are then studied by taking while D remains fixed. The problem in this form owes its inception to McKean-Vaninsky \cite{MV2} who obtained the following result. For with , they showed the same type of diffusion appears in the thermodynamic limit, but with drift arising from the shifted potential being such that the limiting mean-square equals D. Their method of proof predicts the same outcome for , so long as D is smaller than the canonical mean-square , while if , the matter was unresolved. The purpose of this note is to show a type of phase transition takes place in this case: the conditioning is overcome in the limit and one sees the original (stationary) diffusion on the line. The proof employs an entropy inequality due to Csiszár [1]. Received: 9 January 2001 / Accepted: 17 July 2002 Published online: 14 October 2002     

Letter: Exact Solutions for the Interacting Tachyonic–Dark Matter System

We find exact solutions leading to power law accelerated expansion for a homogeneous, isotropic and spatially flat universe, dominated by an interacting mixture of cold dark matter and a tachyonic field such that the ratio of the energy densities of both components at late times is constant and no coincidence problem arises.     

Pair Excitations and the Mean Field Approximation of Interacting Bosons, I

In our previous work (Grillakis et al. in Commun Math Phys 294:273–301, 2010; Adv Math 228:1788–1815, 2011) we introduced a correction to the mean field approximation of interacting Bosons. This correction describes the evolution of pairs of particles that leave the condensate and subsequently evolve on a background formed by the condensate. In Grillakis et al. (Adv Math 228:1788–1815, 2011) we carried out the analysis assuming that the interactions are independent of the number of particles N. Here we consider the case of stronger interactions. We offer a new transparent derivation for the evolution of pair excitations. Indeed, we obtain a pair of linear equations describing their evolution. Furthermore, we obtain a priori estimates independent of the number of particles and use these to compare the exact with the approximate dynamics.     

The Independence on Boundary Conditions for the Thermodynamic Limit of Charged Systems

We study systems containing electrons and nuclei. Based on the fact that the Thermodynamic limit exists for systems with Dirichlet boundary conditions, we prove that the same limit is obtained if one imposes other boundary conditions such as Neumann, periodic, or elastic boundary conditions. The result is proven for all limiting sequences of domains which are obtained by scaling a bounded open set, with smooth boundary, except for isolated edges and corners. Work partially supported by EU grant HPRN-CT-2002-00277.     

The Exact Three-Dimensional Half-Shell t-Matrix for a Sharply Cut-off Coulomb Potential in the Screening Limit

The screening limit of the three-dimensional half-shell t-matrix for a sharply cut-off Coulomb potential is analytically derived without reference to partial wave expansion. The numerical solutions of the three-dimensional Lippmann–Schwinger equation for increasing cut-off radii provide half-shell t-matrices which are in quite a good agreement with the asymptotic values.     

A Lower Bound for the Wehrl Entropy of Quantum Spin with Sharp High-Spin Asymptotics

A lower bound for the Wehrl entropy of a single quantum spin is derived. The high-spin asymptotics of this bound coincides with Liebs conjecture up to, but not including, terms of first and higher order in the inverse spin quantum number. The result presented here may be seen as complementary to the verification of the conjecture in cases of lowest spin by Schupp [Commun. Math. Phys. 207, 481 (1999)]. The present result for the Wehrl-entropy is obtained from interpolating a sharp norm bound that also implies a sharp lower bound for the so-called Rényi-Wehrl entropy with certain indices that are evenly spaced by half of the inverse spin quantum number.     

New Form for the Coulomb Potential in Complex Crystals. Part I

The Coulomb potential is constructed for a crystal with a basis by the method of the Green's functions approximated by the lattice sum of spherically symmetric electron densities of free atoms. The application of the new method with improved convergence of the lattice series in the Green's function has allowed us to obtain an additional term in the electron part of the potential, which describes attraction and can be considered as a potential of the Coulomb hole. The method was applied to calculate the potentials for carbon in the diamond lattice and for TiC solid solution in the direction of four nearest neighbors. Some typical results are presented to illustrate the capabilities of the method.     

Interacting Quantum and Classical Continuous Systems I. The Piecewise Deterministic Dynamics

A mathematical construction of a Markov–Feller process associated with a completely positive coupling between classical and quantum systems is proposed. The example of the free classical particle on the Lobatchevski space Q interacting with the quantum system characterized by coherent states on Q is considered.     

The Population Inversion and the Entropy of a Moving Two-Level Atom in Interaction with a Quantized Field

An atom with only two energy eigenvalues is described by a two-dimensional state space spanned by the two energy eigenstates is called a two-level atom. We consider the interaction between a two-level atom system with a constant velocity. An analytic solution of the systems which interacts with a quantized field is provided. Furthermore, the significant effect of the temperature on the atomic inversion, the purity and the information entropy are discussed in case of the initial state either an exited state or a maximally mixed state. Additionally, the effect of the half wavelengths number of the field-mode is investigated.     

The Gravitating Perfect Fluid-Scalar Field Equations: Quintessence and Tachyonic Matter

The system consisting of a self gravitating perfect fluid and scalar field is considered in detail. The scalar fields considered are the quintessence and tachyonic forms which have important application in cosmology. Mathematical properties of the general system of equations are studied including the algebraic and differential identities as well as the eigenvalue structure. The Cauchy problem for both quintessence and the tachyon is presented. We discuss the initial constraint equations which must be satisfied by the initial data. A Cauchy evolution scheme is presented in the form of a Taylor series about the Cauchy surface. Finally, a simple numerical example is provided to illustrate this scheme.     

Spectral Analysis for Systems of Atoms and Molecules Coupled to the Quantized Radiation Field

We consider systems of static nuclei and electrons – atoms and molecules – coupled to the quantized radiation field. The interactions between electrons and the soft modes of the quantized electromagnetic field are described by minimal coupling, p→p−e A (x), where A(x) is the electromagnetic vector potential with an ultraviolet cutoff. If the interactions between the electrons and the quantized radiation field are turned off, the atom or molecule is assumed to have at least one bound state. We prove that, for sufficiently small values of the fine structure constant α, the interacting system has a ground state corresponding to the bottom of its energy spectrum. For an atom, we prove that its excited states above the ground state turn into metastable states whose life-times we estimate. Furthermore the energy spectrum is absolutely continuous, except, perhaps, in a small interval above the ground state energy and around the threshold energies of the atom or molecule. Received: 3 September 1998 / Accepted: 17 March 1999