251 research outputs found
On the efficient Monte Carlo implementation of path integrals
We demonstrate that the Levy-Ciesielski implementation of Lie-Trotter
products enjoys several properties that make it extremely suitable for
path-integral Monte Carlo simulations: fast computation of paths, fast Monte
Carlo sampling, and the ability to use different numbers of time slices for the
different degrees of freedom, commensurate with the quantum effects. It is
demonstrated that a Monte Carlo simulation for which particles or small groups
of variables are updated in a sequential fashion has a statistical efficiency
that is always comparable to or better than that of an all-particle or
all-variable update sampler. The sequential sampler results in significant
computational savings if updating a variable costs only a fraction of the cost
for updating all variables simultaneously or if the variables are independent.
In the Levy-Ciesielski representation, the path variables are grouped in a
small number of layers, with the variables from the same layer being
statistically independent. The superior performance of the fast sampling
algorithm is shown to be a consequence of these observations. Both mathematical
arguments and numerical simulations are employed in order to quantify the
computational advantages of the sequential sampler, the Levy-Ciesielski
implementation of path integrals, and the fast sampling algorithm.Comment: 14 pages, 3 figures; submitted to Phys. Rev.
Models for local ohmic quantum dissipation
We construct model master equations for local quantum dissipation. The master
equations are in the form of Lindblad generators, with imposed constraints that
the dissipations be strictly linear (i.e. ohmic), isotropic and translationally
invariant. A particular form for is chosen to satisfy the constraints. The
resulting master equations are given in both the Schr\"odinger and Heisenberg
forms. We obtain fluctuation-dissipation relations, and discuss the relaxation
of average kinetic energy to effective thermal equilibrium values. We compare
our results to the Dekker and the Caldeira-Leggett master equations. These
master equations allow a more general approach to quantum dissipation and the
dynamics of quantum coherence to account for the nontrivial system-environment
coupling in a local environment.Comment: 19 pages, REVTEX, PSU/TH/12
Quantum Logic with a Single Trapped Electron
We propose the use of a trapped electron to implement quantum logic
operations. The fundamental controlled-NOT gate is shown to be feasible. The
two quantum bits are stored in the internal and external (motional) degrees of
freedom.Comment: 7 Pages, REVTeX, No Figures, To appear in Phys. Rev.
Proper time and Minkowski structure on causal graphs
For causal graphs we propose a definition of proper time which for small
scales is based on the concept of volume, while for large scales the usual
definition of length is applied. The scale where the change from "volume" to
"length" occurs is related to the size of a dynamical clock and defines a
natural cut-off for this type of clock. By changing the cut-off volume we may
probe the geometry of the causal graph on different scales and therey define a
continuum limit. This provides an alternative to the standard coarse graining
procedures. For regular causal lattice (like e.g. the 2-dim. light-cone
lattice) this concept can be proven to lead to a Minkowski structure. An
illustrative example of this approach is provided by the breather solutions of
the Sine-Gordon model on a 2-dimensional light-cone lattice.Comment: 15 pages, 4 figure
Upon the existence of short-time approximations of any polynomial order for the computation of density matrices by path integral methods
In this article, I provide significant mathematical evidence in support of
the existence of short-time approximations of any polynomial order for the
computation of density matrices of physical systems described by arbitrarily
smooth and bounded from below potentials. While for Theorem 2, which is
``experimental'', I only provide a ``physicist's'' proof, I believe the present
development is mathematically sound. As a verification, I explicitly construct
two short-time approximations to the density matrix having convergence orders 3
and 4, respectively. Furthermore, in the Appendix, I derive the convergence
constant for the trapezoidal Trotter path integral technique. The convergence
orders and constants are then verified by numerical simulations. While the two
short-time approximations constructed are of sure interest to physicists and
chemists involved in Monte Carlo path integral simulations, the present article
is also aimed at the mathematical community, who might find the results
interesting and worth exploring. I conclude the paper by discussing the
implications of the present findings with respect to the solvability of the
dynamical sign problem appearing in real-time Feynman path integral
simulations.Comment: 19 pages, 4 figures; the discrete short-time approximations are now
treated as independent from their continuous version; new examples of
discrete short-time approximations of order three and four are given; a new
appendix containing a short review on Brownian motion has been added; also,
some additional explanations are provided here and there; this is the last
version; to appear in Phys. Rev.
Brownian Motion and Polymer Statistics on Certain Curved Manifolds
We have calculated the probability distribution function G(R,L|R',0) of the
end-to-end vector R-R' and the mean-square end-to-end distance (R-R')^2 of a
Gaussian polymer chain embedded on a sphere S^(D-1) in D dimensions and on a
cylinder, a cone and a curved torus in 3-D.
We showed that: surface curvature induces a geometrical localization area; at
short length the polymer is locally "flat" and (R-R')^2 = L l in all cases; at
large scales, (R-R')^2 is constant for the sphere, it is linear in L for the
cylinder and reaches different constant values for the torus. The cone vertex
induces (function of opening angle and R') contraction of the chain for all
lengths. Explicit crossover formulas are derived.Comment: 9 pages, 4 figures, RevTex, uses amssymb.sty and multicol.sty, to
appear in Phys. Rev
Polaron Variational Methods In The Particle Representation Of Field Theory : I. General Formalism
We apply nonperturbative variational techniques to a relativistic scalar
field theory in which heavy bosons (``nucleons'') interact with light scalar
mesons via a Yukawa coupling. Integrating out the meson field and neglecting
the nucleon vacuum polarization one obtains an effective action in terms of the
heavy particle coordinates which is nonlocal in the proper time. As in
Feynman's polaron approach we approximate this action by a retarded quadratic
action whose parameters are to be determined variationally on the pole of the
two-point function. Several ans\"atze for the retardation function are studied
and for the most general case we derive a system of coupled variational
equations. An approximate analytic solution displays the instability of the
system for coupling constants beyond a critical value.Comment: 33 pages standard LaTeX, 3 uuencoded gzipped postscript figures
embedded with psfig.st
Dynamical Vortices in Superfluid Films
The coupling of vortices to phonons in a superfluid is a gauge coupling
dictated by topology. The density and current response to a moving vortex are
computed and contrasted with the standard backflow picture. Exploiting the
analogy to (2+1)-dimensional electrodynamics, we compute the effective vortex
mass and find it to be logarithmically divergent in the low
frequency limit, leading to a super-Ohmic dissipation in response to an
oscillating superflow. Numerical integration of the nonlinear Schroedinger
equation supports these conclusions. Interaction of vortices and impurities is
also discussed.Comment: 13 pages, 6 figure
Metric Fluctuation Corrections to Hawking Radiation
We study how fluctuations of the black hole geometry affect the properties of
Hawking radiation. Even though we treat the fluctuations classically, we
believe that the results so obtained indicate what might be the effects induced
by quantum fluctuations in a self consistent treatment. To characterize the
fluctuations, we use the model introduced by York in which they are described
by an advanced Vaidya metric with a fluctuating mass. Under the assumption of
spherical symmetry, we solve the equation of null outgoing rays. Then, by
neglecting the greybody factor, we calculate the late time corrections to the
s-wave contributions of the energy flux and the asymptotic spectrum. We find
three kind of modifications. Firstly, the energy flux fluctuates around its
average value with amplitudes and frequencies determined by those of the metric
fluctuations. Secondly, this average value receives two positive contributions
one of which can be reinterpreted as due to the `renormalisation' of the
surface gravity induced by the metric fluctuations. Finally, the asymptotic
spectrum is modified by the addition of terms containing thermal factors in
which the frequency of the metric fluctuations acts as a chemical potential.Comment: 27 pages, 2 figures, LaTeX. Revised versio
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