111 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
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
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.
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
Quantum Transition State Theory for proton transfer reactions in enzymes
We consider the role of quantum effects in the transfer of hyrogen-like
species in enzyme-catalysed reactions. This study is stimulated by claims that
the observed magnitude and temperature dependence of kinetic isotope effects
imply that quantum tunneling below the energy barrier associated with the
transition state significantly enhances the reaction rate in many enzymes. We
use a path integral approach which provides a general framework to understand
tunneling in a quantum system which interacts with an environment at non-zero
temperature. Here the quantum system is the active site of the enzyme and the
environment is the surrounding protein and water. Tunneling well below the
barrier only occurs for temperatures less than a temperature which is
determined by the curvature of potential energy surface near the top of the
barrier. We argue that for most enzymes this temperature is less than room
temperature. For physically reasonable parameters quantum transition state
theory gives a quantitative description of the temperature dependence and
magnitude of kinetic isotope effects for two classes of enzymes which have been
claimed to exhibit signatures of quantum tunneling. The only quantum effects
are those associated with the transition state, both reflection at the barrier
top and tunneling just below the barrier. We establish that the friction due to
the environment is weak and only slightly modifies the reaction rate.
Furthermore, at room temperature and for typical energy barriers environmental
degrees of freedom with frequencies much less than 1000 cm do not have a
significant effect on quantum corrections to the reaction rate.Comment: Aspects of the article are discussed at
condensedconcepts.blogspot.co
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.
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
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