3,607 research outputs found
Schulman Replies
This is a reply to a comment of Casati, Chirikov and Zhirov (PRL 85, 896
(2000)) on PRL 83, 5419 (1999).
The suitability of the particlar two-time boundary value problem used in the
earlier PRL is argued
Stability of quantum breathers
Using two methods we show that a quantized discrete breather in a 1-D lattice
is stable. One method uses path integrals and compares correlations for a
(linear) local mode with those of the quantum breather. The other takes a local
mode as the zeroth order system relative to which numerical, cutoff-insensitive
diagonalization of the Hamiltonian is performed.Comment: 4 pages, 3 figure
Analysis of a three-component model phase diagram by Catastrophe Theory
We analyze the thermodynamical potential of a lattice gas model with three
components and five parameters using the methods of Catastrophe Theory. We find
the highest singularity, which has codimension five, and establish its
transversality. Hence the corresponding seven-degree Landau potential, the
canonical form Wigwam or , constitutes the adequate starting point to
study the overall phase diagram of this model.Comment: 16 pages, Latex file, submitted to Phys. Rev.
A new representation for non--local operators and path integrals
We derive an alternative representation for the relativistic non--local
kinetic energy operator and we apply it to solve the relativistic Salpeter
equation using the variational sinc collocation method. Our representation is
analytical and does not depend on an expansion in terms of local operators. We
have used the relativistic harmonic oscillator problem to test our formula and
we have found that arbitrarily precise results are obtained, simply increasing
the number of grid points. More difficult problems have also been considered,
observing in all cases the convergence of the numerical results. Using these
results we have also derived a new representation for the quantum mechanical
Green's function and for the corresponding path integral. We have tested this
representation for a free particle in a box, recovering the exact result after
taking the proper limits, and we have also found that the application of the
Feynman--Kac formula to our Green's function yields the correct ground state
energy. Our path integral representation allows to treat hamiltonians
containing non--local operators and it could provide to the community a new
tool to deal with such class of problems.Comment: 9 pages ; 1 figure ; refs added ; title modifie
Location- and observation time-dependent quantum-tunneling
We investigate quantum tunneling in a translation invariant chain of
particles. The particles interact harmonically with their nearest neighbors,
except for one bond, which is anharmonic. It is described by a symmetric double
well potential. In the first step, we show how the anharmonic coordinate can be
separated from the normal modes. This yields a Lagrangian which has been used
to study quantum dissipation. Elimination of the normal modes leads to a
nonlocal action of Caldeira-Leggett type. If the anharmonic bond defect is in
the bulk, one arrives at Ohmic damping, i.e. there is a transition of a
delocalized bond state to a localized one if the elastic constant exceeds a
critical value . The latter depends on the masses of the bond defect.
Superohmic damping occurs if the bond defect is in the site at a finite
distance from one of the chain ends. If the observation time is smaller
than a characteristic time , depending on the location M of the
defect, the behavior is similar to the bulk situation. However, for tunneling is never suppressed.Comment: 17 pages, 2 figure
J-factors of short DNA molecules
The propensity of short DNA sequences to convert to the circular form is
studied by a mesoscopic Hamiltonian method which incorporates both the bending
of the molecule axis and the intrinsic twist of the DNA strands. The base pair
fluctuations with respect to the helix diameter are treated as path
trajectories in the imaginary time path integral formalism. The partition
function for the sub-ensemble of closed molecules is computed by imposing chain
ends boundary conditions both on the radial fluctuations and on the angular
degrees of freedom. The cyclization probability, the J-factor, proves to be
highly sensitive to the stacking potential, mostly to its nonlinear parameters.
We find that the J-factor generally decreases by reducing the sequence length (
N ) and, more significantly, below N = 100 base pairs. However, even for very
small molecules, the J-factors remain sizeable in line with recent experimental
indications. Large bending angles between adjacent base pairs and anharmonic
stacking appear as the causes of the helix flexibility at short length scales.Comment: The Journal of Chemical Physics - May 2016 ; 9 page
Feynman's Path Integrals and Bohm's Particle Paths
Both Bohmian mechanics, a version of quantum mechanics with trajectories, and
Feynman's path integral formalism have something to do with particle paths in
space and time. The question thus arises how the two ideas relate to each
other. In short, the answer is, path integrals provide a re-formulation of
Schroedinger's equation, which is half of the defining equations of Bohmian
mechanics. I try to give a clear and concise description of the various aspects
of the situation.Comment: 4 pages LaTeX, no figures; v2 shortened a bi
Roughening transition, surface tension and equilibrium droplet shapes in a two-dimensional Ising system
The exact surface tension for all angles and temperatures is given for the two-dimensional square Ising system with anisotropic nearest-neighbour interactions. Using this in the Wulff construction, droplet shapes are computed and illustrated. Letting temperature approach zero allows explicit study of the roughening transition in this model. Results are compared with those of the solid-on-solid approximation
On hemispheric differences in evoked potentials to speech stimuli
Confirmation is provided for the belief that evoked potentials may reflect differences in hemispheric functioning that are marginal at best. Subjects were right-handed and audiologically normal men and women, and responses were recorded using standard EEG techniques. Subjects were instructed to listen for the targets while laying in a darkened sound booth. Different stimuli, speech and tone signals, were used. Speech sounds were shown to evoke a response pattern that resembles that to tone or clicks. Analysis of variances on peak amplitude and latency measures showed no significant differences between hemispheres, however, a Wilcoxon test showed significant differences in hemispheres for certain target tasks
A path integral leading to higher-order Lagrangians
We consider a simple modification of standard phase-space path integrals and
show that it leads in configuration space to Lagrangians depending also on
accelerations.Comment: 6 page
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