Iterative evaluation of the path integral for a system coupled to an anharmonic bath

Journal URL: http://jcp.aip.org/jcp/staff.js

Iterative algorithm versus analytic solutions of the parametrically driven dissipative quantum harmonic oscillator

We consider the Brownian motion of a quantum mechanical particle in a one-dimensional parabolic potential with periodically modulated curvature under the influence of a thermal heat bath. Analytic expressions for the time-dependent position and momentum variances are compared with results of an iterative algorithm, the so-called quasiadiabatic propagator path integral algorithm (QUAPI). We obtain good agreement over an extended range of parameters for this spatially continuous quantum system. These findings indicate the reliability of the algorithm also in cases for which analytic results may not be available a priori.Comment: 15 pages including 11 figures, one reference added, minor typos correcte

Dynamical simulation of transport in one-dimensional quantum wires

Transport of single-channel spinless interacting fermions (Luttinger liquid) through a barrier has been studied by numerically exact quantum Monte Carlo methods. A novel stochastic integration over the real-time paths allows for direct computation of nonequilibrium conductance and noise properties. We have examined the low-temperature scaling of the conductance in the crossover region between a very weak and an almost insulating barrier.Comment: REVTex, 4 pages, 2 uuencoded figures (submitted to Phys. Rev. Lett.

Comparative study of semiclassical approaches to quantum dynamics

Quantum states can be described equivalently by density matrices, Wigner functions or quantum tomograms. We analyze the accuracy and performance of three related semiclassical approaches to quantum dynamics, in particular with respect to their numerical implementation. As test cases, we consider the time evolution of Gaussian wave packets in different one-dimensional geometries, whereby tunneling, resonance and anharmonicity effects are taken into account. The results and methods are benchmarked against an exact quantum mechanical treatment of the system, which is based on a highly efficient Chebyshev expansion technique of the time evolution operator.Comment: 32 pages, 8 figures, corrected typos and added references; version as publishe

Random Series and Discrete Path Integral methods: The Levy-Ciesielski implementation

We perform a thorough analysis of the relationship between discrete and series representation path integral methods, which are the main numerical techniques used in connection with the Feynman-Kac formula. First, a new interpretation of the so-called standard discrete path integral methods is derived by direct discretization of the Feynman-Kac formula. Second, we consider a particular random series technique based upon the Levy-Ciesielski representation of the Brownian bridge and analyze its main implementations, namely the primitive, the partial averaging, and the reweighted versions. It is shown that the n=2^k-1 subsequence of each of these methods can also be interpreted as a discrete path integral method with appropriate short-time approximations. We therefore establish a direct connection between the discrete and the random series approaches. In the end, we give sharp estimates on the rates of convergence of the partial averaging and the reweighted Levy-Ciesielski random series approach for sufficiently smooth potentials. The asymptotic rates of convergence are found to be O(1/n^2), in agreement with the rates of convergence of the best standard discrete path integral techniques.Comment: 20 pages, 4 figures; the two equations before Eq. 14 are corrected; other typos are remove

Multicanonical Multigrid Monte Carlo

To further improve the performance of Monte Carlo simulations of first-order phase transitions we propose to combine the multicanonical approach with multigrid techniques. We report tests of this proposition for the $d$-dimensional $\Phi^4$ field theory in two different situations. First, we study quantum tunneling for $d = 1$ in the continuum limit, and second, we investigate first-order phase transitions for $d = 2$ in the infinite volume limit. Compared with standard multicanonical simulations we obtain improvement factors of several resp. of about one order of magnitude.Comment: 12 pages LaTex, 1 PS figure appended. FU-Berlin preprint FUB-HEP 9/9

Cumulant Expansions and the Spin-Boson Problem

The dynamics of the dissipative two-level system at zero temperature is studied using three different cumulant expansion techniques. The relative merits and drawbacks of each technique are discussed. It is found that a new technique, the non-crossing cumulant expansion, appears to embody the virtues of the more standard cumulant methods.Comment: 26 pages, LaTe

Low-temperature dynamical simulation of spin-boson systems

The dynamics of spin-boson systems at very low temperatures has been studied using a real-time path-integral simulation technique which combines a stochastic Monte Carlo sampling over the quantum fluctuations with an exact treatment of the quasiclassical degrees of freedoms. To a large degree, this special technique circumvents the dynamical sign problem and allows the dynamics to be studied directly up to long real times in a numerically exact manner. This method has been applied to two important problems: (1) crossover from nonadiabatic to adiabatic behavior in electron transfer reactions, (2) the zero-temperature dynamics in the antiferromagnetic Kondo region 1/2<K<1 where K is Kondo's parameter.Comment: Phys. Rev. B (in press), 28 pages, 6 figure

A time-frequency analysis perspective on Feynman path integrals

The purpose of this expository paper is to highlight the starring role of time-frequency analysis techniques in some recent contributions concerning the mathematical theory of Feynman path integrals. We hope to draw the interest of mathematicians working in time-frequency analysis on this topic, as well as to illustrate the benefits of this fruitful interplay for people working on path integrals.Comment: 26 page

Suppression of decoherence via strong intra-environmental coupling

We examine the effects of intra-environmental coupling on decoherence by constructing a low temperature spin--spin-bath model of an atomic impurity in a Debye crystal. The impurity interacts with phonons of the crystal through anti-ferromagnetic spin-spin interactions. The reduced density matrix of the central spin representing the impurity is calculated by dynamically integrating the full Schroedinger equation for the spin--spin-bath model for different thermally weighted eigenstates of the spin-bath. Exact numerical results show that increasing the intra-environmental coupling results in suppression of decoherence. This effect could play an important role in the construction of solid state quantum devices such as quantum computers.Comment: 4 pages, 3 figures, Revtex fil