5,311 research outputs found
Thermal effects on chaotic directed transport
We study a chaotic ratchet system under the influence of a thermal
environment. By direct integration of the Lindblad equation we are able to
analyze its behavior for a wide range of couplings with the environment, and
for different finite temperatures. We observe that the enhancement of the
classical and quantum currents due to temperature depend strongly on the
specific properties of the system. This makes difficult to extract universal
behaviors. We have also found that there is an analogy between the effects of
the classical thermal noise and those of the finite size. These results
open many possibilities for their testing and implementation in kicked BECs and
cold atoms experiments.Comment: 5 pages, 4 figure
Quantum analysis of a nonlinear microwave cavity-embedded dc SQUID displacement detector
We carry out a quantum analysis of a dc SQUID mechanical displacement
detector, comprising a SQUID with mechanically compliant loop segment, which is
embedded in a microwave transmission line resonator. The SQUID is approximated
as a nonlinear, current dependent inductance, inducing an external flux
tunable, nonlinear Duffing self-interaction term in the microwave resonator
mode equation. Motion of the compliant SQUID loop segment is transduced
inductively through changes in the external flux threading SQUID loop, giving a
ponderomotive, radiation pressure type coupling between the microwave and
mechanical resonator modes. Expressions are derived for the detector signal
response and noise, and it is found that a soft-spring Duffing self-interaction
enables a closer approach to the displacement detection standard quantum limit,
as well as cooling closer to the ground state
Exact and approximate many-body dynamics with stochastic one-body density matrix evolution
We show that the dynamics of interacting fermions can be exactly replaced by
a quantum jump theory in the many-body density matrix space. In this theory,
jumps occur between densities formed of pairs of Slater determinants, , where each state evolves according to the Stochastic
Schr\"odinger Equation (SSE) given in ref. \cite{Jul02}. A stochastic
Liouville-von Neumann equation is derived as well as the associated
Bogolyubov-Born-Green-Kirwood-Yvon (BBGKY) hierarchy. Due to the specific form
of the many-body density along the path, the presented theory is equivalent to
a stochastic theory in one-body density matrix space, in which each density
matrix evolves according to its own mean field augmented by a one-body noise.
Guided by the exact reformulation, a stochastic mean field dynamics valid in
the weak coupling approximation is proposed. This theory leads to an
approximate treatment of two-body effects similar to the extended
Time-Dependent Hartree-Fock (Extended TDHF) scheme. In this stochastic mean
field dynamics, statistical mixing can be directly considered and jumps occur
on a coarse-grained time scale. Accordingly, numerical effort is expected to be
significantly reduced for applications.Comment: 12 pages, 1 figur
Symmetry projection schemes for Gaussian Monte Carlo methods
A novel sign-free Monte Carlo method for the Hubbard model has recently been
proposed by Corney and Drummond. High precision measurements on small clusters
show that ground state correlation functions are not correctly reproduced. We
argue that the origin of this mismatch lies in the fact that the low
temperature density matrix does not have the symmetries of the Hamiltonian.
Here we show that supplementing the algorithm with symmetry projection schemes
provides reliable and accurate estimates of ground state properties.Comment: 10 pages, 3 figure
Opacity of electromagnetically induced transparency for quantum fluctuations
We analyze the propagation of a pair of quantized fields inside a medium of
three-level atoms in configuration. We calculate the stationary
quadrature noise spectrum of the field after propagating through the medium, in
the case where the probe field is in a squeezed state and the atoms show
electromagnetically induced transparency (EIT). We find an oscillatory transfer
of the initial quantum properties between the probe and pump fields which is
most strongly pronounced when both fields have comparable Rabi frequencies.
This implies that the quantum state measured after propagation can be
completely different from the initial state, even though the mean values of the
field are unaltered
Numerical Methods for Stochastic Differential Equations
Stochastic differential equations (sdes) play an important role in physics
but existing numerical methods for solving such equations are of low accuracy
and poor stability. A general strategy for developing accurate and efficient
schemes for solving stochastic equations in outlined here. High order numerical
methods are developed for integration of stochastic differential equations with
strong solutions. We demonstrate the accuracy of the resulting integration
schemes by computing the errors in approximate solutions for sdes which have
known exact solutions
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