476 research outputs found
Quantum interference in the classically forbidden region: a parametric oscillator
We study tunneling between period two states of a parametrically modulated
oscillator. The tunneling matrix element is shown to oscillate with the varying
frequency of the modulating field. The effect is due to spatial oscillations of
the wave function and the related interference in the classically forbidden
region. The oscillations emerge already in the ground state of the oscillator
Hamiltonian in the rotating frame, which is quartic in the momentum.Comment: Submitted to PR
Relaxation of a qubit measured by a driven Duffing oscillator
We investigate the relaxation of a superconducting qubit for the case when
its detector, the Josephson bifurcation amplifier, remains latched in one of
its two (meta)stable states of forced vibrations. The qubit relaxation rates
are different in different states. They can display strong dependence on the
qubit frequency and resonant enhancement, which is due to quasienergy
resonances. Coupling to the driven oscillator changes the effective temperature
of the qubit.Comment: To appear in Phys. Rev. A (2010
Exponential peak and scaling of work fluctuations in modulated systems
We extend the stationary-state work fluctuation theorem to periodically
modulated nonlinear systems. Such systems often have coexisting stable periodic
states. We show that work fluctuations sharply increase near a kinetic phase
transition where the state populations are close to each other. The work
variance is proportional here to the reciprocal rate of interstate switching.
We also show that the variance displays scaling with the distance to a
bifurcation point and find the critical exponent for a saddle-node bifurcation
Observable and hidden singular features of large fluctuations in nonequilibrium systems
We study local features, and provide a topological insight into the global
structure of the probability density distribution and of the pattern of the
optimal paths for large rare fluctuations away from a stable state. In contrast
to extremal paths in quantum mechanics, the optimal paths do {\it not}
encounter caustics. We show how this occurs, and what, instead of caustics, are
the experimentally observable singularities of the pattern. We reveal the
possibility for a caustic and a switching line to start at a saddle point, and
discuss the consequences.Comment: 10 pages, 3 ps figures by request, LaTeX Article Format (In press,
Phys. Lett. A
Multiphoton antiresonance in large-spin systems
We study nonlinear response of a spin with easy-axis anisotropy. The
response displays sharp dips or peaks when the modulation frequency is
adiabatically swept through multiphoton resonance. The effect is a consequence
of a special symmetry of the spin dynamics in a magnetic field for the
anisotropy energy . The occurrence of the dips or peaks is
determined by the spin state. Their shape strongly depends on the modulation
amplitude. Higher-order anisotropy breaks the symmetry, leading to sharp steps
in the response as function of frequency. The results bear on the dynamics of
molecular magnets in a static magnetic field.Comment: Submitted to PR
Diffusion-induced dephasing in nanomechanical resonators
We study resonant response of an underdamped nanomechanical resonator with
fluctuating frequency. The fluctuations are due to diffusion of molecules or
microparticles along the resonator. They lead to broadening and change of shape
of the oscillator spectrum. The spectrum is found for the diffusion confined to
a small part of the resonator and where it occurs along the whole nanobeam. The
analysis is based on extending to the continuous limit, and appropriately
modifying, the method of interfering partial spectra. We establish the
conditions of applicability of the fluctuation-dissipation relations between
the susceptibility and the power spectrum. We also find where the effect of
frequency fluctuations can be described by a convolution of the spectra without
these fluctuations and with them as the only source of the spectral broadening.Comment: 10 page
Theory of Second and Higher Order Stochastic Processes
This paper presents a general approach to linear stochastic processes driven
by various random noises. Mathematically, such processes are described by
linear stochastic differential equations of arbitrary order (the simplest
non-trivial example is , where is not a Gaussian white
noise). The stochastic process is discretized into time-steps, all possible
realizations are summed up and the continuum limit is taken. This procedure
often yields closed form formulas for the joint probability distributions.
Completely worked out examples include all Gaussian random forces and a large
class of Markovian (non-Gaussian) forces. This approach is also useful for
deriving Fokker-Planck equations for the probability distribution functions.
This is worked out for Gaussian noises and for the Markovian dichotomous noise.Comment: 35 pages, PlainTex, accepted for publication in Phys Rev. E
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