Exact classical and quantum solutions for a covariant oscillator near the black hole horizon in Stueckelberg-Horwitz-Piron theory

We found exact solutions for canonical classical and quantum dynamics for general relativity in Horwitz general covariance theory. These solutions can be obtained by solving the generalized geodesic equation and Schrödinger-Stueckelberg-Horwitz-Piron (SHP) wave equation for a simple harmonic oscillator in the background of a two dimensional dilaton black hole spacetime metric. We proved the existence of an orthonormal basis of eigenfunctions for generalized wave equation. This basis functions form an orthogonal and normalized (orthonormal) basis for an appropriate Hilbert space. The energy spectrum has a mixed spectrum with one conserved momentum p according to a quantum number n. To find the ground state energy we used a variational method with appropriate boundary conditions. A set of mode decomposed wave functions and calculated for the Stueckelberg-Schrodinger equation on a general five dimensional blackhole spacetime in Hamilton gauge.     

Diffusive corrections to asymptotics of a strong-field quantum transport equation

The asymptotic analysis of a linear high-field Wigner-BGK equation is developed by a modified Chapman-Enskog procedure. By an expansion of the unknown Wigner function in powers of the Knudsen number ?, evolution equations are derived for the terms of zeroth and first order in ?. In particular, a quantum drift-diffusion equation for the position density of electrons, with an ?-order correction on the field terms, is obtained. Well-posedness and regularity of the approximate problems are established, and a rigorous proof that the difference between exact and asymptotic solutions is of order ?², uniformly in time and for arbitrary initial data is given.     

Partial Boolean Functions With Exact Quantum Query Complexity One

We provide two sufficient and necessary conditions to characterize any n-bit partial Boolean function with exact quantum query complexity 1. Using the first characterization, we present all n-bit partial Boolean functions that depend on n bits and can be computed exactly by a 1-query quantum algorithm. Due to the second characterization, we construct a function F that maps any n-bit partial Boolean function to some integer, and if an n-bit partial Boolean function f depends on k bits and can be computed exactly by a 1-query quantum algorithm, then F(f) is non-positive. In addition, we show that the number of all n-bit partial Boolean functions that depend on k bits and can be computed exactly by a 1-query quantum algorithm is not bigger than an upper bound depending on n and k. Most importantly, the upper bound is far less than the number of all n-bit partial Boolean functions for all efficiently big n.     

量子Generalized Reed-Solomon码

构造出了一族量子纠错码,这族码具有参数［［n,n-2k,k+1］］_q,是q维量子系统上的码,q是任意素数的幂.这族码的最小距离达到了理论上限,因此,以码距来说,它是最优的.证明了当2≤n≤q或者q²-q+2≤n≤q²时,码都是存在的. 关键词： 量子Generalized Reed-Solomon码 量子MDS码 量子纠错码 量子信息     

Number-resolved master equation approach to quantum measurement and quantum transport

In addition to the well-known Landauer–Büttiker scattering theory and the nonequilibrium Green’s function technique for mesoscopic transports, an alternative (and very useful) scheme is quantum master equation approach. In this article, we review the particle-number (n)-resolved master equation (n-ME) approach and its systematic applications in quantum measurement and quantum transport problems. The n-ME contains rich dynamical information, allowing efficient study of topics such as shot noise and full counting statistics analysis. Moreover, we also review a newly developed master equation approach (and its n-resolved version) under self-consistent Born approximation. The application potential of this new approach is critically examined via its ability to recover the exact results for noninteracting systems under arbitrary voltage and in presence of strong quantum interference, and the challenging non-equilibrium Kondo effect.     

On the integration of some classes of (<Emphasis Type="Italic">n</Emphasis>+1)-dimensional nonlinear equations of mathematical physics

This paper presents a method for construction of the families of particular solutions to some new classes of (n+1)-dimensional nonlinear partial differential equations (PDE). The method is based on the specific link between algebraic matrix equations and PDEs. Admittable solutions depend on arbitrary functions of n variables. Examples of deformed Burgers-type equations are given.     

Revisiting non-degenerate parametric down-conversion

The quantum dynamics of a two-mode non-resonant parametric down-conversion process is studied by recasting the time evolution equations for the basic operators in an equivalent spin equation form with simpler exact solutions for a pump field with harmonic time dependence. Expectation values of suitable operators for studying important features such as squeezing and quantum revivals are presented in simple forms.      

External gravitational interactions in quantum field theory

We consider the renormalization of Green's functions of λφ⁴ quantum field theory in an external gravitational field specified by the metric tensor g^μν(y). Green's functions Γ^(n,3) describing the interaction of j scalar particles to arbitrary order n in the gravitational field are shown to be made finite by the standard renormalizations of the flatspace theory and a renormalization of the coefficient of the improvement term in the action functional. These results in φ⁴ theory can be extended to all renormalizable field theories.     

Unveiling Operator Growth Using Spin Correlation Functions

In this paper, we study non-equilibrium dynamics induced by a sudden quench of strongly correlated Hamiltonians with all-to-all interactions. By relying on a Sachdev-Ye-Kitaev (SYK)-based quench protocol, we show that the time evolution of simple spin-spin correlation functions is highly sensitive to the degree of k-locality of the corresponding operators, once an appropriate set of fundamental fields is identified. By tracking the time-evolution of specific spin-spin correlation functions and their decay, we argue that it is possible to distinguish between operator-hopping and operator growth dynamics; the latter being a hallmark of quantum chaos in many-body quantum systems. Such an observation, in turn, could constitute a promising tool to probe the emergence of chaotic behavior, rather accessible in state-of-the-art quench setups.     

The role of particular collision and radiative processes in recombination

Rate equations for level populations of atomic hydrogen are solved to obtain collisional-radiative recombination coefficients. Several particular collision and radiative processes entering the rate equations have been accounted for or have been suppressed in order to obtain information on how strongly the solution depends on the different assumptions. Under certain conditions the results differ by orders of magnitude. The results also vary strongly with the number of quantum levelsp entering the rate equations. The critical quantum numbern ^* which defines the limit for partial L.T.E. cannot be considered as the critical number of rate equations above which the population coefficients become independent ofp.     

Far-from-equilibrium quantum many-body dynamics

A theory of real-time quantum many-body dynamics is evaluated in detail. It is based on a generating functional of correlation functions where the closed time contour extends only to a given time. Expanding the contour from this time to a later time leads to a dynamic flow of the generating functional. This flow describes the dynamics of the system and has an explicit causal structure. In the present work it is evaluated within a vertex expansion of the effective action leading to time-evolution equations for Green functions. These equations are applicable for strongly interacting systems as well as for studying the late-time behavior of non-equilibrium time evolution. For the specific case of a bosonic $\mathcal{N}$ -component φ ⁴-theory with contact interactions an s-channel truncation is identified to yield equations identical to those derived from the 2PI effective action in next-to-leading order of a $1/\mathcal{N}$ expansion. The presented approach allows to directly obtain non-perturbative dynamic equations beyond the widely used 2PI approximations.     

Enhancement of stationary state quantum discord in Tavis-Cummings model by nonlinear Kerr-like medium

We investigate the influence of nonlinear Kerr-like medium and dipole-dipole interaction on the dynamics of quantum discord in Tavis-Cummings model with phase decoherence. We show that in the resonance case (i) atom-field quantum discord rapidly decays with phase decoherence and doesn't exist the stationary state quantum discord, but the stationary state quantum discord appears if we choose the suitable values of Kerr coefficient χ and dipole-dipole interaction Ω, (ii) the quantum discord of two atoms survives in the stationary state and the amount of stationary state quantum discord could be improved by adjusting the values of χ and Ω. In the non-resonance case, the arbitrary bipartite quantum discord of the system could not be completely destroyed by the phase decoherence and can be improved by applying nonlinear Kerr-like medium and dipole-dipole interaction.     

A nonperturbative solution to the Dyson-Schwinger-equations of QCD

This is the first of two papers in which we discuss a nonperturbatively modified solution to the Euclidean Dyson-Schwinger equations for the 7 superficially divergent proper verticesΓ of QCD. It takes the formΣ _n g ²ⁿ Γ( ⁿ ) where eachΓ( ⁿ ) approaches its perturbative form at large momenta. At lower momenta, it differs from that form by an additional non-analyticg ² dependence through a dynamical mass scaleb, proportional toΛ _qcd and associated with a pole dependence on the momentum invariants. In the zeroth-order two-point functions, these nonperturbative modifications amount to a generalized Schwinger mechanism, leading to propagators without particle poles. The termsΓ(⁰), representing the Feynman rules of the modified iterative solution, can become self-consistent in the DS equations through a mechanism of “nonperturbative logarithms” which we explain. The mechanism is tied to the presence of divergent loops, and thus represents a pure quantum effect, similar to quantum anomalies. It restricts formation of nonperturbativeΓ(⁰)'s to the 7 primitively divergent vertices, thus escaping the infinite nature of the DS hierarchy. In a given loop order, the self-consistency problem reduces to a finite set of algebraic equations.     

Lagrangian approach for dark soliton in nonlocal nonlinear media

We theoretically investigate the dynamics of dark solitons as well as their interaction in nonlocal media. Approximate equations describing the evolution of the beams are obtained via suitable trial functions of amplitude u and refractive index n in an averaged Lagrangian. Our results reveal that out-of-phase dark solitons can evolve into stable bound states in nonlocal materials. Moreover, it is found that the separations in the bound state monotonically increase with the degree of nonlocality in nonlocal limit. These results are in excellent agreement with the numerical simulations.     

Generalized tripartite scheme for sharing arbitrary 2n-qudit state

Utilizing three non-maximally entangled qutrit pairs as quantum channels, we first propose a generalized tripartite scheme for sharing an arbitrary two-qutrit state with generalized Bell-state measurements. In the scheme if and only if the two recipients collaborate together, they can recover the split qutrit state with the probability determined uniquely by the smallest coefficients of the non-maximally entangled pairs. Afterwards, we further extend the scheme for sharing an arbitrary 2n-qudit state by taking 3n non-maximally entangled qudit pairs as quantum channels. Moreover, the scheme success probability relative to the inherent entanglement in quantum channels and its structure is simply discussed.     

Quantum cosmology inR 1×S 1×S n space time

Classical and quantum cosmological aspects for (n + 2) dimensional anisotropic spherically symmetric space-time with topology of (n + 1) spaceS ¹×S ⁿ have been studied. The Lorentzian field equations are reduced to an autonomous system by a change of field variables and are discussed near the critical points. The path integral expression for propagation amplitude is converted to a single ordinary integration over the lapse function by the usual technique and is evaluated in terms of Bessel functions.     

Exact hole-bound states for semiconductor quantum wells with arbitrary potential profiles

An efficient numerical-analytical method for finding confined and continuum states in quantum-well systems with arbitrary potential profiles, described by coupled Schrödinger equations, is presented. The method is based on the analytical properties of the wave functions, in particular, the power series representation of solutions of the corresponding coupled differential equations. Using only the general properties of the coefficients of a system of an arbitrary number of coupled Schrödinger equations, and imposing for definiteness the simplest boundary conditions, we derive exact expressions for the wave functions and present methods for accurate calculations of the energies and wave functions of confined states and of the wave functions of continuum states in quantum wells. The method is applied to the calculation of the dispersion of hole bound states in a single GaAs quantum well with truncated parabolic confining potentials of different strengths. The results are compared with data available from previous calculations.     

Coherence theory and coherence phenomena in a closed spin‐1/2 system

A simplified Heisenberg spin model is studied in order to examine the idea of decoherence in closed quantum systems. For this purpose, we present a quantifiable definition to quantum coherence Ξ, and discuss in some detail a general coherence theory and its elementary results. As expected, decoherence is understood as a statistical process that is caused by the dynamics of the system, similar to the growth of entropy. It appears that coherence is an important measure that helps to understand quantum properties of a system, e.g., the decoherence time can be derived from the coherence function Ξ(t), but not from the entropy dynamics. Moreover, the concept of decoherence time is applicable in closed and finite systems. However, in most cases, the decay of off‐diagonal elements differs from the usual exp(‐t/τ_d) behaviour. For concreteness, we report the form of decoherence time τ_d in a finite Heisenberg model with respect to the number of particles N, density n_ρ, spatial dimension D and ? in a η/r^?‐type of potential.