158 research outputs found
Landau-Zener problem for energies close to potential crossing points
We examine one overlooked in previous investigations aspect of well - known
Landau - Zener (LZ) problem, namely, the behavior in the intermediate, i.e.
close to a crossing point, energy region, when all four LZ states are coupled
and should be taken into account. We calculate the 4 x 4 connection matrix in
this intermediate energy region, possessing the same block structure as the
known connection matrices for the tunneling and in the over-barrier regions of
the energy, and continously matching those in the corresponding energy regions.Comment: 5 pages, 1 figur
Inertial particles driven by a telegraph noise
We present a model for the Lagrangian dynamics of inertial particles in a
compressible flow, where fluid velocity gradients are modelled by a telegraph
noise. The model allows for an analytic investigation of the role of time
correlation of the flow in the aggregation-disorder transition of inertial
particle. The dependence on Stokes and Kubo numbers of the Lyapunov exponent of
particle trajectories reveals the presence of a region in parameter space (St,
Ku) where the leading Lyapunov exponent changes sign, thus signaling the
transition. The asymptotics of short and long-correlated flows are discussed,
as well as the fluid-tracer limit.Comment: 8 pages, 6 figure
Dynamic and spectral mixing in nanosystems
In the framework of simple spin-boson Hamiltonian we study an interplay
between dynamic and spectral roots to stochastic-like behavior. The Hamiltonian
describes an initial vibrational state coupled to discrete dense spectrum
reservoir. The reservoir states are formed by three sequences with rationally
independent periodicities typical for vibrational states in many nanosize
systems. We show that quantum evolution of the system is determined by a
dimensionless parameter which is characteristic number of the reservoir states
relevant for the initial vibrational level dynamics. Our semi-quantitative
analytic results are confirmed by numerical solution of the equation of motion.
We anticipate that predicted in the paper both kinds of stochastic-like
behavior (namely, due to spectral mixing and recurrence cycle dynamic mixing)
can be observed by femtosecond spectroscopy methods in nanosystems.Comment: 6 pages, 4 figure
Loschmidt echo and stochastic-like quantum dynamics of nano-particles
We investigate time evolution of prepared vibrational state (system) coupled
to a reservoir with dense spectrum of its vibrational states. We assume that
the reservoir has an equidistant spectrum, and the system - reservoir coupling
matrix elements are independent of the reservoir states. The analytical
solution manifests three regimes of the evolution for the system: (I) weakly
damped oscillations; (II) multicomponent Loschmidt echo in recurrence cycles;
(III) overlapping recurrence cycles. We find the characteristic critical values
of the system - reservoir coupling constant for the transitions between these
regimes. Stochastic dynamics occurs in the regime (III) due to inevoidably in
any real system coarse graining of time or energy measurements, or initial
condition uncertainty. Even though a specific toy model is investigated here,
when properly interpreted it yields quite reasonable description for a variety
of physically relevant phenomena.Comment: 8 pages, 3 figure
Coherent oscillations and incoherent tunnelling in one - dimensional asymmetric double - well potential
For a model 1d asymmetric double-well potential we calculated so-called
survival probability (i.e. the probability for a particle initially localised
in one well to remain there). We use a semiclassical (WKB) solution of
Schroedinger equation. It is shown that behaviour essentially depends on
transition probability, and on dimensionless parameter which is a ratio of
characteristic frequencies for low energy non-linear in-well oscillations and
inter wells tunnelling. For the potential describing a finite motion
(double-well) one has always a regular behaviour. For the small value of the
parameter there is well defined resonance pairs of levels and the survival
probability has coherent oscillations related to resonance splitting. However
for the large value of the parameter no oscillations at all for the survival
probability, and there is almost an exponential decay with the characteristic
time determined by Fermi golden rule. In this case one may not restrict oneself
to only resonance pair levels. The number of perturbed by tunnelling levels
grows proportionally to the value of this parameter (by other words instead of
isolated pairs there appear the resonance regions containing the sets of
strongly coupled levels). In the region of intermediate values of the parameter
one has a crossover between both limiting cases, namely the exponential decay
with subsequent long period recurrent behaviour.Comment: 19 pages, 7 figures, Revtex, revised version. Accepted to Phys. Rev.
Effects of tunnelling and asymmetry for system-bath models of electron transfer
We apply the newly derived nonadiabatic golden-rule instanton theory to
asymmetric models describing electron-transfer in solution. The models go
beyond the usual spin-boson description and have anharmonic free-energy
surfaces with different values for the reactant and product reorganization
energies. The instanton method gives an excellent description of the behaviour
of the rate constant with respect to asymmetry for the whole range studied. We
derive a general formula for an asymmetric version of Marcus theory based on
the classical limit of the instanton and find that this gives significant
corrections to the standard Marcus theory. A scheme is given to compute this
rate based only on equilibrium simulations. We also compare the rate constants
obtained by the instanton method with its classical limit to study the effect
of tunnelling and other quantum nuclear effects. These quantum effects can
increase the rate constant by orders of magnitude.Comment: 10 pages, 3 figure
Decoherence and Dissipation in Quantum Two-State Systems
The Brownian dynamics of the density operator for a quantum system
interacting with a classical heat bath is described using a stochastic,
non-linear Liouville equation obtained from a variational principle. The
environment's degrees of freedom are simulated by classical harmonic
oscillators, while the dynamical variables of the quantum system are two
non-hermitian "square root operators" defined by a Gauss-like decomposition of
the density operator. The rate of the noise-induced transitions is expressed as
a function of the environmental spectral density, and is discussed for the case
of the white noise and blackbody radiation. The result is compared with the
rate determined by a quantum environment, calculated by partial tracing in the
whole Hilbert space. The time-dependence of the von Neumann entropy and of the
dissipated energy is obtained numerically for a system of two quantum states.
These are the ground and first excited state of the center of mass vibrations
for an ion confined in a harmonic trap.Comment: 17 pages, LaTex, 3 postscript figures; replaced to correct typo in
Eq. (5
Electron-lattice kinetics of metals heated by ultrashort laser pulses
We propose a kinetic model of transient nonequilibrium phenomena in metals
exposed to ultrashort laser pulses when heated electrons affect the lattice
through direct electron-phonon interaction. This model describes the
destruction of a metal under intense laser pumping. We derive the system of
equations for the metal, which consists of hot electrons and a cold lattice.
Hot electrons are described with the help of the Boltzmann equation and
equation of thermoconductivity. We use the equations of motion for lattice
displacements with the electron force included. The lattice deformation is
estimated immediately after the laser pulse up to the time of electron
temperature relaxation. An estimate shows that the ablation regime can be
achieved.Comment: 7 pages; Revtex. to appear in JETP 88, #1 (1999
DIFFUSIVE TRANSPORT IN A ONE DIMENSIONAL DISORDERED POTENTIAL INVOLVING CORRELATIONS
This article deals with transport properties of one dimensional Brownian
diffusion under the influence of a correlated quenched random force,
distributed as a two-level Poisson process. We find in particular that large
time scaling laws of the position of the Brownian particle are analogous to the
uncorrelated case. We discuss also the probability distribution of the
stationary flux going through a sample between two prescribed concentrations,
which differs significantly from the uncorrelated case.Comment: 9 pages, figures are not include
Spin dynamics in finite cyclic XY model
Evolution of the z-component of a single spin in the finite cyclic XY spin
1/2 chain is studied. Initially one selected spin is polarized while other
spins are completely unpolarized and uncorrelated. Polarization of the selected
spin as a function of time is proportional to the autocorrelation function at
infinite temperature. Initialization of the selected spin gives rise to two
wave packets moving in opposite directions and winding over the circle. We
express the correlation function as a series in winding number and derive
tractable approximations for each term. This allows to give qualitative
explanation and quantitative description to various finite-size effects such as
partial revivals and transition from regular to erratic behavior.Comment: v2: substantially extended; v3: references added, accepted to Phys.
Rev.
- …