4,182 research outputs found
Survival and Nonescape Probabilities for Resonant and Nonresonant Decay
In this paper we study the time evolution of the decay process for a particle
confined initially in a finite region of space, extending our analysis given
recently (Phys. Rev. Lett. 74, 337 (1995)). For this purpose, we solve exactly
the time-dependent Schroedinger equation for a finite-range potential. We
calculate and compare two quantities: (i) the survival probability S(t), i.e.,
the probability that the particle is in the initial state after a time t; and
(ii) the nonescape probability P(t), i.e., the probability that the particle
remains confined inside the potential region after a time t. We analyze in
detail the resonant and nonresonant decay. In the former case, after a very
short time, S(t) and P(t) decay exponentially, but for very long times they
decay as a power law, albeit with different exponents. For the nonresonant case
we obtain that both quantities differ initially. However, independently of the
resonant and nonresonant character of the initial state we always find a
transition to the ground state of the system which indicates a process of
``loss of memory'' in the decay.Comment: 26 pages, RevTex file, figures available upon request from
[email protected] (To be published in Annals of Physics
Injection statistics simulator for dynamic analysis of noise in mesoscopic devices
We present a model for electron injection from thermal reservoirs which is
applied to particle simulations of one-dimensional mesoscopic conductors. The
statistics of injected carriers is correctly described from nondegenerate to
completely degenerate conditions. The model is validated by comparing Monte
Carlo simulations with existing analytical results for the case of ballistic
conductors. An excellent agreement is found for average and noise
characteristics, in particular, the fundamental unities of electrical and
thermal conductances are exactly reproduced.Comment: 4 pages, revtex, 4 PS figures, accepted Semicond. Sci. Techno
Anticipated synchronization in coupled inertia ratchets with time-delayed feedback: a numerical study
We investigate anticipated synchronization between two periodically driven
deterministic, dissipative inertia ratchets that are able to exhibit directed
transport with a finite velocity. The two ratchets interact through an
unidirectional delay coupling: one is acting as a master system while the other
one represents the slave system. Each of the two dissipative deterministic
ratchets is driven externally by a common periodic force. The delay coupling
involves two parameters: the coupling strength and the (positive-valued) delay
time. We study the synchronization features for the unbounded, current carrying
trajectories of the master and the slave, respectively, for four different
strengths of the driving amplitude. These in turn characterize differing phase
space dynamics of the transporting ratchet dynamics: regular, intermittent and
a chaotic transport regime. We find that the slave ratchet can respond in
exactly the same way as the master will respond in the future, thereby
anticipating the nonlinear directed transport
ac-driven Brownian motors: a Fokker-Planck treatment
We consider a primary model of ac-driven Brownian motors, i.e., a classical
particle placed in a spatial-time periodic potential and coupled to a heat
bath. The effects of fluctuations and dissipations are studied by a
time-dependent Fokker-Planck equation. The approach allows us to map the
original stochastic problem onto a system of ordinary linear algebraic
equations. The solution of the system provides complete information about
ratchet transport, avoiding such disadvantages of direct stochastic
calculations as long transients and large statistical fluctuations. The
Fokker-Planck approach to dynamical ratchets is instructive and opens the space
for further generalizations
New models for two real scalar fields and their kinklike solutions
In this work we study the presence of kinks in models described by two real
scalar fields in bi-dimensional space-time. We generate new two-field models,
constructed from distinct but important one-field models, and we solve them
with techniques that we introduce in the current work. We illustrate the
results with several examples of current interest to high energy physics.Comment: 8 pages, 6 figures; To appear in Adv. High Energy Phy
Two-point one-dimensional - interactions: non-abelian addition law and decoupling limit
In this contribution to the study of one dimensional point potentials, we
prove that if we take the limit on a potential of the type
, we
obtain a new point potential of the type , when and are related to , , and
by a law having the structure of a group. This is the Borel subgroup of
. We also obtain the non-abelian addition law from the
scattering data. The spectra of the Hamiltonian in the exceptional cases
emerging in the study are also described in full detail. It is shown that for
the , values of the couplings the
singular Kurasov matrices become equivalent to Dirichlet at one side of the
point interaction and Robin boundary conditions at the other side
Doorway States and Billiards
Whenever a distinct state is immersed in a sea of complicated and dense
states, the strength of the distinct state, which we refer to as a doorway, is
distributed in their neighboring states. We analyze this mechanism for 2-D
billiards with different geometries. One of them is symmetric and integrable,
another is symmetric but chaotic, and the third has a capricious form. The fact
that the doorway-state mechanism is valid for such highly diverse cases, proves
that it is robust.Comment: 7 pages, 6 figures, Accepted in Proceedings of "Symmetries in
Nature", Symposium in Memoriam Marcos Moshinsk
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