Quantum kinetic theory of trapped particles in a strong electromagnetic field

The idea of treating quantum systems by semiclassical representations using effective quantum potentials (forces) has been successfully applied in equilibrium by many authors, see e.g. [D. Bohm, Phys. Rev. 85 (1986) 166 and 180; D.K. Ferry, J.R. Zhou, Phys. Rev. B 48 (1993) 7944; A.V. Filinov, M. Bonitz, W. Ebeling, J. Phys. A 36 (2003) 5957 and references cited therein]. Here, this idea is extended to nonequilibrium quantum systems in an external field. A gauge-invariant quantum kinetic theory for weakly inhomogeneous charged particle systems in a strong electromagnetic field is developed within the framework of nonequilibrium Green’s functions. The equation for the spectral density is simplified by introducing a classical (local) form for the kinetics. Nonlocal quantum effects are accounted for in this way by replacing the bare external confinement potential with an effective quantum potential. The equation for this effective potential is identified and solved for weak inhomogeneity in the collisionless limit. The resulting nonequilibrium spectral function is used to determine the density of states and the modification of the Born collision operator in the kinetic equation for the Wigner function due to quantum confinement effects.     

Method of green's functions in the theory of quantum kinetic equations. II

The kinetic and antikinetic equations are obtained for the single-particle Wigner function in the context of the method of Green's time-temperature functions for an inhomogeneous system of weakly interacting particles situated in a time-dependent electric field. The kinetic equation is derived here from the equation of motion for Green's function, satisfying the causality condition.     

Ladder Invariants and Coherent States for Time-Dependent Non-Hermitian Hamiltonians

International Journal of Theoretical Physics - We extend the Dodonov–Malkin–Man’ko–Trifonov (DMMT) invariant method (Malkin et al. Phys. Rev. D 2, 1371 1, J. Math. Phys. 14,...     

Wave Functions for Time-Dependent Dirac Equation under GUP

In this work, the time-dependent Dirac equation is investigated under generalized uncertainty principle(GUP) framework. It is possible to construct the exact solutions of Dirac equation when the time-dependent potentials satisfied the proper conditions. In(1+1) dimensions, the analytical wave functions of the Dirac equation under GUP have been obtained for the two kinds time-dependent potentials.     

Soliton-like solutions of certain types of nonlinear diffusion-reaction equations with variable coefficient

With a view to exploring new soliton-like solutions of certain types of nonlinear diffusion-reaction (DR) equations with a variable coefficient, we demonstrate the viability of a method which is the combination of both the symbolic computation technique of Gao and Tian [Y.T. Gao, B. Tian, Comput. Phys. Commun. 133 (2001) 158] and auxiliary equation method of Sirendaoreji [Sirendaoreji, Phys. Lett. A 356 (2006) 124] and used recently for the KdV equation. In particular, the DR equations with quadratic and cubic nonlinearities with a time-dependent velocity in the convective flux term are studied and the existence of soliton-like solutions is shown.     

Derivation of generalized quantum jump operators and comparison of the microscopic single photon detector models

The recent experiment of Parigi et al. [Science 317, 1890 (2007)] shows, in agreement with theory, that subtraction of one photon can increase the expectation value of the number of photons in the thermal state. This observation agrees with the standard photon counting model in which the quantum jump superoperator (QJS) gives a count rate proportional to the number of photons. An alternate model for indirect photon counting has been introduced by Dodonov et al. [Phys. Rev. A 72, 023816 (2005)]. In their model the count rate is proportional to the probability that there are photons in the cavity, and the cavity field is bidirectionally coupled with a two state quantum system which is unidirectionally coupled to a counting device. We give a consistent first principle derivation of the QJSs for the indirect photon counting scheme and establish the complete relations between the physical measurement setup and the QJSs. It is shown that the time-dependent probability for photoelectron emission event must include normalization of the conditional probability. This normalization was neglected in the previous derivation of the QJSs. We include the normalization and obtain the correct photoelectron emission rates and the correct QJSs and show in which coupling parameter regimes these QJSs are applicable. Our analytical results are compared with the exact numerical solution of the Lindblad equation of the system. The derived QJSs enable analysis of experimental photon count rates in a case where a one-to-one correspondence does not exist between the decay of photons and the detection events.     

Lattice calculations of the photoionization of Li

Calculations are presented for the double photoionization (with excitation) and triple photoionization of the Li atom. The motion of all three electrons is treated equally by solving the time-dependent Schr?dinger equation in nine dimensions. A radial lattice is used to represent three of the nine dimensions, while a coupled channel expansion is used to represent the other six dimensions. Probabilities for photoionization are obtained by t--> infinity projection onto fully antisymmetric spatial and spin functions. Double photoionization cross sections for lithium leaving the ion in the 1s, 2s, and 2p states are presented. Good agreement is found with the measurements of Huang et al. [Phys. Rev. A 59, 3397 (1999)]] for the total double photoionization cross section and with the measurements of Wehlitz et al. [Phys. Rev. Lett. 81, 1813 (1998)]] for the triple photoionization cross section.     

Exact analytic relation between quantum defects and scattering phases with applications to Green’s functions in quantum defect theory

The relation between the quantum defects, , and scattering phases, , in the single-channel Quantum Defect Theory (QDT) is discussed with an emphasis on their analyticity properties for both integer and noninteger values of the orbital angular momentum parameter . To derive an accurate relation between and for asymptotically-Coulomb potentials, the QDT is formally developed for the Whittaker equation in its general form “perturbed” by an additional short-range potential. The derived relations demonstrate that is a complex function for above-threshold energies, which is analogous to the fact that is complex for below-threshold energies. The QDT Green's function, , of the “perturbed” Whittaker equation is parameterized by the functions and for the continuous and discrete spectrum domains respectively, and a number of representations for are presented for the general case of noninteger . Our derivations and analyses provide a more general justification of known results for nonrelativistic and relativistic cases involving Coulomb potentials and for a Coulomb plus point dipole potential. Received 25 June 1999     

Attosecond resolved electron release in two-color near-threshold photoionization of N2

We have simulated two-color photoionization of N(2) by solving the time-dependent Schr?dinger equation with a simple model accounting for the correlated vibronic dynamics of the molecule and of the ion N(2)(+). Our results, in very good agreement with recent experiments [Haessler et al., Phys. Rev. A 80, 011404 (2009)], show how a resonance embedded in the molecular continuum dramatically affects the phases of the two-photon transition amplitudes. In addition, we introduce a formal relation between these measurable phases and the photoelectron release time, opening the way to attosecond time-resolved measurements, equivalent to double-slit experiments in the time domain.     

Localized partial traps in diffusion processes and random walks

Reaction-diffusion equations, in which the reaction is described by a sink term consisting of a sum of delta functions, are studied. It is shown that the Laplace transform of the reactive Green's function can be analytically expressed in terms of the Green's function for diffusion in the absence of reaction. Moreover, a simple relation between the Green's functions satisfying the radiation boundary condition and the reflecting boundary condition is obtained. Several applications are presented and the formalism is used to establish the relationship between the time-dependent geminate recombination yield and the bimolecular reaction rate for diffusion-influenced reactions. Finally, an analogous development for lattice random walks is presented.     

Helium atom in the monochromatic electromagnetic field

We apply a non-perturbative procedure for the calculation of the total photoionization cross-section of two-electron atomic systems. The procedure is based on the Floquet-Fourier representation of the time-dependent Schr?dinger equation. With the use of the Hylleraas-type basis functions, the total photoionization cross-sections obtained are within the accuracy of a fraction of a percent, which, we believe, is the most accurate estimate for the cross-sections available. The total photoionization cross-sections for neutral helium deviate notably from the benchmark experimental data [J.A.R. Samson et al., J. Phys. B 27, 887 (1994)].     

d''''Alembert方程的含时Green函数和推迟势

运用傅里叶变换、留数定理求解了达朗贝尔方程的标势格林函数和矢势格林函数，给出了达朗贝尔方程特解的格林函数法求解过程。     

Method of Green's functions in the theory of quantum kinetic equations. I

The solution of the dynamic equation is strongly degenerate for systems with an infinite number of degrees of freedom. A causality principle is stated, whereby the particular solution of the dynamic equation, which is at the same time a solution of the kinetic equation, can be selected. The principle is applied here to the multitime formalism of correlation functions. A basis is thus obtained for the method of Green's time-temperature functions in the theory of kinetic equations.The author thanks all those who have discussed the topics in this paper with him, particularly V. L. Bonch-Bruevich, D.A. Kirzhnits, V.M. Fain, E.S. Fradkin, and A. S. Shekhter.     

Supersymmetric WKB Approximation of Anharmonic Potential V(r)=ar2+br-4+cr-6

This article uses the supersymmetric WKB approximation to obtain the approximate energy levels and wave functions of the anharmonic potential V(r) = ar2 br-4 cr-6 in order to tesify the correctness between [Phys.Lett. A 170 (1992) 335] and the paper written by M. Landtman [Phys. Lett. A 175 (1993) 147].     

Symmetry of the Unsteady Linearized Boltzmann Equation in a Fixed Bounded Domain

A symmetric relation between time-dependent problems described by the linearized Boltzmann equation is obtained for a gas in a fixed bounded domain. General representations of the total mass, momentum, and energy in the domain, as well as their fluxes through the boundary, in terms of an appropriate Green function are derived from that relation. Several application examples are presented. Similarities to the fluctuation–dissipation theorem in the linear response theory and its generalization to gas systems of arbitrary Knudsen numbers are also discussed. The present paper is an extension of the previous work of the author (Takata in J. Stat. Phys. 136: 751–784, 2009) to time-dependent problems.     

2D H-Atom in an Arbitrary Magnetic Field via Pseudoperturbation Expansions Through the Quantum Number l

The pseudoperturbative shifted-1 expansion technique is introduced to determine nodeless states of the 2D Schrodinger equation with arbitrary cylindrically symmetric potentials. Exact energy eigenvalues and eigenfunctions for the 2D Coulomb and harmonic oscillator potentials are reproduced. Moreover, exact energy eigenvalues, compared with those obtained by numerical solution (V.M. Villalba and R. Pino, J. Phys.: Condens. Matter 8 (1996) 80671, were obtained for the hybrid of the 20 Coulomli and oscillator potentials.     

On self-consistent approximations for random anharmonic systems

A model with random 1-, 2-, and 3-point potentials is used to study the elementary excitations in substitutionally disordered crystals. The equations of motion for the 1- and 2-point Green's functionsG(1),G(12) are derived and averaged over the ensemble of random configurations. An extension of the coherent potential method is proposed, which leads to a self-consistent set of equations for the averaged 1- and 2-point Green's functions, including corresponding conditional averages. The theory takes into account that randomness effects the anharmonic interactions both via the explicit configuration dependence of the cubic vertices and via the implicit dependence through the Green's functions. The final equations take a similar form as in the usual CPA if the harmonic potential of the pure system and the harmonic single-site impurity potential are replaced by corresponding functionals of averaged and conditionally averaged 1- and 2-point functions, and the definition of the single-site mass-operator is appropriately generalized.Work supported by the Deutsche ForschungsgemeinschaftExtract from thesis, D 26     

A note on failure of the ladder approximation to QCD

In this Letter we show that the claim made in [V. Gogohia, Phys. Lett. B 611 (2005) 129] that the ladder approximation to QCD is internally inconsistent is incorrect. The incorrect conclusion in [V. Gogohia, Phys. Lett. B 611 (2005) 129] is based on the incorrect use of a QED-type Ward–Takahashi relation, which does not hold in the ladder approximation to QCD. We give a proof for this fact.     

Polynomial pseudosupersymmetry underlying a two-level atom in an external electromagnetic field

We study chains of transformations introduced in B.F. Samsonov and V.V. Shamshutdinova: J. Phys. A: Math. Gen. 38 (2005) 4715, in order to obtain electric fields with a time-dependent frequency for which the equation of motion of a two-level atom in the presence of these fields can be solved exactly. We show that a polynomial pseudosupersymmetry may be associated to such chains. Presented at the 3rd International Workshop “Pseudo-Hermitian Hamiltonians in Quantum Physics”, Istanbul, Turkey, June 20–22, 2005.     

Slow algebraic relaxation in quartic potentials and related results

We present a detailed report [see S. Sen et al., Phys. Rev. Lett. 77, 4855 (1996)] of our numerical and analytical studies on the relaxation of a classical particle in the potentials V(x)= +/-x(2)/2+x(4)/4. Both of the approaches confirm that at all temperatures, the relaxation functions (e.g., velocity relaxation function and position relaxation function) decay asymptotically in time t as sin(omega(0)t)/t. Numerically calculated power spectra of the relaxation functions show a gradual transition with increasing temperature from a single sharp peak located at the harmonic frequency omega(0) to a broad continuous band. The 1/t relaxation is also found when V(x) is a polynomial in powers of x(2) with a nonvanishing coefficient accompanying the x(4) term in V(x). Numerical calculations show that in the cases in which the leading term in V(x) behaves as x(2n) with integer n, the asymptotic relaxation exhibits 1/t(phi) decay where phi =1/(n-1). We briefly discuss the analytical approaches to relaxation studies in these strongly anharmonic systems using direct solution of the equation of motion and using the continued fraction formalism approach for relaxation studies. We show that the study of the dynamics of strongly anharmonic oscillators poses unique difficulties when studied via the continued fraction or any other time-series construction based approaches. We close with comments on the physical processes in which the insights presented in this work may be applicable.