4,800 research outputs found
Directed transport in periodically rocked random sawtooth potentials
We study directed transport of overdamped particles in a periodically rocked
random sawtooth potential. Two transport regimes can be identified which are
characterized by a nonzero value of the average velocity of particles and a
zero value, respectively. The properties of directed transport in these regimes
are investigated both analytically and numerically in terms of a random
sawtooth potential and a periodically varying driving force. Precise conditions
for the occurrence of transition between these two transport regimes are
derived and analyzed in detail.Comment: 18 pages, 7 figure
Quantum ratchet transport with minimal dispersion rate
We analyze the performance of quantum ratchets by considering the dynamics of
an initially localized wave packet loaded into a flashing periodic potential.
The directed center-of-mass motion can be initiated by the uniform modulation
of the potential height, provided that the modulation protocol breaks all
relevant time- and spatial reflection symmetries. A poor performance of quantum
ratchet transport is characterized by a slow net motion and a fast diffusive
spreading of the wave packet, while the desirable optimal performance is the
contrary. By invoking a quantum analog of the classical P\'eclet number, namely
the quotient of the group velocity and the dispersion of the propagating wave
packet, we calibrate the transport properties of flashing quantum ratchets and
discuss the mechanisms that yield low-dispersive directed transport.Comment: 6 pages; 3 figures; 1 tabl
Biased diffusion in a piecewise linear random potential
We study the biased diffusion of particles moving in one direction under the
action of a constant force in the presence of a piecewise linear random
potential. Using the overdamped equation of motion, we represent the first and
second moments of the particle position as inverse Laplace transforms. By
applying to these transforms the ordinary and the modified Tauberian theorem,
we determine the short- and long-time behavior of the mean-square displacement
of particles. Our results show that while at short times the biased diffusion
is always ballistic, at long times it can be either normal or anomalous. We
formulate the conditions for normal and anomalous behavior and derive the laws
of biased diffusion in both these cases.Comment: 11 pages, 3 figure
Unfolding quantum master equation into a system of real-valued equations: computationally effective expansion over the basis of generators
Dynamics of an open -state quantum system is typically modeled with a
Markovian master equation describing the evolution of the system's density
operator. By using generators of group as a basis, the density operator
can be transformed into a real-valued 'Bloch vector'. The Lindbladian, a
super-operator which serves a generator of the evolution, %in the master
equation, can be expanded over the same basis and recast in the form of a real
matrix. Together, these expansions result is a non-homogeneous system of
real-valued linear differential equations for the Bloch vector. Now one
can, e.g., implement a high-performance parallel simplex algorithm to find a
solution of this system which guarantees exact preservation of the norm and
Hermiticity of the density matrix. However, when performed in a straightforward
way, the expansion turns to be an operation of the time complexity
. The complexity can be reduced when the number of
dissipative operators is independent of , which is often the case for
physically meaningful models. Here we present an algorithm to transform quantum
master equation into a system of real-valued differential equations and
propagate it forward in time. By using a scalable model, we evaluate
computational efficiency of the algorithm and demonstrate that it is possible
to handle the model system with states on a single node of a
computer cluster
- …