318 research outputs found
Test of Quantum Action for Inverse Square Potential
We present a numerical study of the quantum action previously introduced as a
parametrisation of Q.M. transition amplitudes. We address the questions: Is the
quantum action possibly an exact parametrisation in the whole range of
transition times ()? Is the presence of potential terms beyond
those occuring in the classical potential required? What is the error of the
parametrisation estimated from the numerical fit? How about convergence and
stability of the fitting method (dependence on grid points, resolution, initial
conditions, internal precision etc.)? Further we compare two methods of
numerical determination of the quantum action: (i) global fit of the Q.M.
transition amplitudes and (ii) flow equation. As model we consider the inverse
square potential, for which the Q.M. transition amplitudes are analytically
known. We find that the relative error of the parametrisation starts from zero
at T=0 increases to about at and then decreases to zero
when . Second, we observe stability of the quantum action under
variation of the control parameters. Finally, the flow equation method works
well in the regime of large giving stable results under variation of
initial data and consistent with the global fit method.Comment: Text (LaTeX), Figures(ps
Complex Effective Path: A Semi-Classical Probe of Quantum Effects
We discuss the notion of an effective, average, quantum mechanical path which
is a solution of the dynamical equations obtained by extremizing the quantum
effective action. Since the effective action can, in general, be complex, the
effective path will also, in general, be complex. The imaginary part of the
effective action is known to be related to the probability of particle creation
by an external source and hence we expect the imaginary part of the effective
path also to contain information about particle creation. We try to identify
such features using simple examples including that of effective path through
the black hole horizon leading to thermal radiation. Implications of this
approach are discussed.Comment: 20 pages; no figures; to appear in Phys.Rev.
Estimating Temperature Fluctuations in the Early Universe
A lagrangian for the essence field is constructed for a constant scalar
potential and its form determined when the scale factor was very small compared
to the present epoch but very large compared to the inflationary epoch. This
means that one is already in an expanding and flat universe. The form is
similar to that of an oscillator with time-dependent frequency. Expansion is
naturally built into the theory with the existence of growing classical
solutions of the scale factor. The formalism allows one to estimate
fluctuations of the temperature of the background radiation in these early
stages (compared to the present epoch) of the universe. If the temperature at
time is and at time the temperature is
(), then for small times, the probability for the logarithm of
inverse temperature evolution can be estimated to be given by
where
, is the Planck mass and Planck's constant and the
speed of light has been put equal to unity. There is the further possibility
that a single scalar field may suffice for an inflationary scenario as well as
the dark matter and dark energy realms.Comment: 8 pages, Revtex, title,abstract and format changed for journal
publication,no change in basic results, clarifications and a figure added.
Keywords: physics of the early universe,inflation, dark matter theory, dark
energy theory. PACS: 95.35.+d ; 95.36.+x ; 98.80.Cq ; 98.80.-
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
Quantum mechanical path integrals and thermal radiation in static curved spacetimes
The propagator of a spinless particle is calculated from the quantum
mechanical path integral formalism in static curved spacetimes endowed with
event-horizons. A toy model, the Gui spacetime, and the 2D and 4D Schwarzschild
black holes are considered. The role of the topology of the coordinates
configuration space is emphasised in this framework. To cover entirely the
above spacetimes with a single set of coordinates, tortoise coordinates are
extended to complex values. It is shown that the homotopic properties of the
complex tortoise configuration space imply the thermal behaviour of the
propagator in these spacetimes. The propagator is calculated when end points
are located in identical or distinct spacetime regions separated by one or
several event-horizons. Quantum evolution through the event-horizons is shown
to be unitary in the fifth variable.Comment: 22 pages, 10 figure
p-Adic and Adelic Harmonic Oscillator with Time-Dependent Frequency
The classical and quantum formalism for a p-adic and adelic harmonic
oscillator with time-dependent frequency is developed, and general formulae for
main theoretical quantities are obtained. In particular, the p-adic propagator
is calculated, and the existence of a simple vacuum state as well as adelic
quantum dynamics is shown. Space discreteness and p-adic quantum-mechanical
phase are noted.Comment: 10 page
Free energy of the Fr\"ohlich polaron in two and three dimensions
We present a novel Path Integral Monte Carlo scheme to solve the Fr\"ohlich
polaron model. At intermediate and strong electron-phonon coupling, the polaron
self-trapping is properly taken into account at the level of an effective
action obtained by a preaveraging procedure with a retarded trial action. We
compute the free energy at several couplings and temperatures in three and two
dimensions. Our results show that the accuracy of the Feynman variational upper
bound for the free energy is always better than 5% although the thermodynamics
derived from it is not correct. Our estimates of the ground state energies
demonstrate that the second cumulant correction to the variational upper bound
predicts the self energy to better than 1% at intermediate and strong coupling.Comment: RevTeX 7 pages 3 figures, revised versio
Natural boundaries for the Smoluchowski equation and affiliated diffusion processes
The Schr\"{o}dinger problem of deducing the microscopic dynamics from the
input-output statistics data is known to admit a solution in terms of Markov
diffusions. The uniqueness of solution is found linked to the natural
boundaries respected by the underlying random motion. By choosing a reference
Smoluchowski diffusion process, we automatically fix the Feynman-Kac potential
and the field of local accelerations it induces. We generate the family of
affiliated diffusions with the same local dynamics, but different inaccessible
boundaries on finite, semi-infinite and infinite domains. For each diffusion
process a unique Feynman-Kac kernel is obtained by the constrained (Dirichlet
boundary data) Wiener path integration.As a by-product of the discussion, we
give an overview of the problem of inaccessible boundaries for the diffusion
and bring together (sometimes viewed from unexpected angles) results which are
little known, and dispersed in publications from scarcely communicating areas
of mathematics and physics.Comment: Latex file, Phys. Rev. E 49, 3815-3824, (1994
Exact expression for the diffusion propagator in a family of time-dependent anharmonic potentials
We have obtained the exact expression of the diffusion propagator in the
time-dependent anharmonic potential . The
underlying Euclidean metric of the problem allows us to obtain analytical
solutions for a whole family of the elastic parameter a(t), exploiting the
relation between the path integral representation of the short time propagator
and the modified Bessel functions. We have also analyzed the conditions for the
appearance of a non-zero flow of particles through the infinite barrier located
at the origin (b<0).Comment: RevTex, 19 pgs. Accepted in Physical Review
Quantum singular oscillator as a model of two-ion trap: an amplification of transition probabilities due to small time variations of the binding potential
Following the paper by M. Combescure [Ann. Phys. (NY) 204, 113 (1990)], we
apply the quantum singular time dependent oscillator model to describe the
relative one dimensional motion of two ions in a trap. We argue that the model
can be justified for low energy excited states with the quantum numbers , provided that the dimensionless constant characterizing the
strength of the repulsive potential is large enough, . Time
dependent Gaussian-like wave packets generalizing odd coherent states of the
harmonic oscillator, and excitation number eigenstates are constructed. We show
that the relative motion of the ions, in contradistinction to its center of
mass counterpart, is extremely sensitive to the time dependence of the binding
harmonic potential, since the large value of results in a significant
amplification of the transition probabilities between energy eigenstate even
for slow time variations of the frequency.Comment: 19 pages, LaTeX, 5 eps-figures, to appear on Phys. Rev. A, one
reference correcte
- …