10,999 research outputs found
Quantum Brownian motion of multipartite systems and their entanglement dynamics
We solve the model of N quantum Brownian oscillators linearly coupled to an
environment of quantum oscillators at finite temperature, with no extra
assumptions about the structure of the system-environment coupling. Using a
compact phase-space formalism, we give a rather quick and direct derivation of
the master equation and its solutions for general spectral functions and
arbitrary temperatures. Since our framework is intrinsically nonperturbative,
we are able to analyze the entanglement dynamics of two oscillators coupled to
a common scalar field in previously unexplored regimes, such as off resonance
and strong coupling.Comment: 10 pages, 6 figure
Nonequilibrium Dynamics of Charged Particles in an Electromagnetic Field: Causal and Stable Dynamics from 1/c Expansion of QED
We derive from a microscopic Hamiltonian a set of stochastic equations of
motion for a system of spinless charged particles in an electromagnetic (EM)
field based on a consistent application of a dimensionful 1/c expansion of
quantum electrodynamics (QED). All relativistic corrections up to order 1/c^3
are captured by the dynamics, which includes electrostatic interactions
(Coulomb), magnetostatic backreaction (Biot-Savart), dissipative backreaction
(Abraham-Lorentz) and quantum field fluctuations at zero and finite
temperatures. With self-consistent backreaction of the EM field included we
show that this approach yields causal and runaway-free equations of motion,
provides new insights into charged particle backreaction, and naturally leads
to equations consistent with the (classical) Darwin Hamiltonian and has quantum
operator ordering consistent with the Breit Hamiltonian. To order 1/c^3 the
approach leads to a nonstandard mass renormalization which is associated with
magnetostatic self-interactions, and no cutoff is required to prevent runaways.
Our new results also show that the pathologies of the standard Abraham-Lorentz
equations can be seen as a consequence of applying an inconsistent (i.e.
incomplete, mixed-order) expansion in 1/c, if, from the start, the analysis is
viewed as generating a low-energy effective theory rather than an exact
solution. Finally, we show that the 1/c expansion within a Hamiltonian
framework yields well-behaved noise and dissipation, in addition to the
multiple-particle interactions.Comment: 17 pages, 2 figure
Non-Markovian Dynamics and Entanglement of Two-level Atoms in a Common Field
We derive the stochastic equations and consider the non-Markovian dynamics of
a system of multiple two-level atoms in a common quantum field. We make only
the dipole approximation for the atoms and assume weak atom-field interactions.
From these assumptions we use a combination of non-secular open- and
closed-system perturbation theory, and we abstain from any additional
approximation schemes. These more accurate solutions are necessary to explore
several regimes: in particular, near-resonance dynamics and low-temperature
behavior. In detuned atomic systems, small variations in the system energy
levels engender timescales which, in general, cannot be safely ignored, as
would be the case in the rotating-wave approximation (RWA). More problematic
are the second-order solutions, which, as has been recently pointed out, cannot
be accurately calculated using any second-order perturbative master equation,
whether RWA, Born-Markov, Redfield, etc.. This latter problem, which applies to
all perturbative open-system master equations, has a profound effect upon
calculation of entanglement at low temperatures. We find that even at zero
temperature all initial states will undergo finite-time disentanglement
(sometimes termed "sudden death"), in contrast to previous work. We also use
our solution, without invoking RWA, to characterize the necessary conditions
for Dickie subradiance at finite temperature. We find that the subradiant
states fall into two categories at finite temperature: one that is temperature
independent and one that acquires temperature dependence. With the RWA there is
no temperature dependence in any case.Comment: 17 pages, 13 figures, v2 updated references, v3 clarified results and
corrected renormalization, v4 further clarified results and new Fig. 8-1
Energy Conversion Alternatives Study (ECAS), General Electric Phase 1. Volume 2: Advanced Energy Conversion Systems. Part 2: Closed Turbine Cycles
For abstract, see N76-23680
Initial state preparation with dynamically generated system-environment correlations
The dependence of the dynamics of open quantum systems upon initial
correlations between the system and environment is an utterly important yet
poorly understood subject. For technical convenience most prior studies assume
factorizable initial states where the system and its environments are
uncorrelated, but these conditions are not very realistic and give rise to
peculiar behaviors. One distinct feature is the rapid build up or a sudden jolt
of physical quantities immediately after the system is brought in contact with
its environments. The ultimate cause of this is an initial imbalance between
system-environment correlations and coupling. In this note we demonstrate
explicitly how to avoid these unphysical behaviors by proper adjustments of
correlations and/or the coupling, for setups of both theoretical and
experimental interest. We provide simple analytical results in terms of
quantities that appear in linear (as opposed to affine) master equations
derived for factorized initial states.Comment: 6 pages, 2 figure
The equilibrium states of open quantum systems in the strong coupling regime
In this work we investigate the late-time stationary states of open quantum
systems coupled to a thermal reservoir in the strong coupling regime. In
general such systems do not necessarily relax to a Boltzmann distribution if
the coupling to the thermal reservoir is non-vanishing or equivalently if the
relaxation timescales are finite. Using a variety of non-equilibrium formalisms
valid for non-Markovian processes, we show that starting from a product state
of the closed system = system + environment, with the environment in its
thermal state, the open system which results from coarse graining the
environment will evolve towards an equilibrium state at late-times. This state
can be expressed as the reduced state of the closed system thermal state at the
temperature of the environment. For a linear (harmonic) system and environment,
which is exactly solvable, we are able to show in a rigorous way that all
multi-time correlations of the open system evolve towards those of the closed
system thermal state. Multi-time correlations are especially relevant in the
non-Markovian regime, since they cannot be generated by the dynamics of the
single-time correlations. For more general systems, which cannot be exactly
solved, we are able to provide a general proof that all single-time
correlations of the open system evolve to those of the closed system thermal
state, to first order in the relaxation rates. For the special case of a
zero-temperature reservoir, we are able to explicitly construct the reduced
closed system thermal state in terms of the environmental correlations.Comment: 20 pages, 2 figure
The Rotating-Wave Approximation: Consistency and Applicability from an Open Quantum System Analysis
We provide an in-depth and thorough treatment of the validity of the
rotating-wave approximation (RWA) in an open quantum system. We find that when
it is introduced after tracing out the environment, all timescales of the open
system are correctly reproduced, but the details of the quantum state may not
be. The RWA made before the trace is more problematic: it results in incorrect
values for environmentally-induced shifts to system frequencies, and the
resulting theory has no Markovian limit. We point out that great care must be
taken when coupling two open systems together under the RWA. Though the RWA can
yield a master equation of Lindblad form similar to what one might get in the
Markovian limit with white noise, the master equation for the two coupled
systems is not a simple combination of the master equation for each system, as
is possible in the Markovian limit. Such a naive combination yields inaccurate
dynamics. To obtain the correct master equation for the composite system a
proper consideration of the non-Markovian dynamics is required.Comment: 17 pages, 0 figures
Particle dynamics inside shocks in Hamilton-Jacobi equations
Characteristics of a Hamilton-Jacobi equation can be seen as action
minimizing trajectories of fluid particles. For nonsmooth "viscosity"
solutions, which give rise to discontinuous velocity fields, this description
is usually pursued only up to the moment when trajectories hit a shock and
cease to minimize the Lagrangian action. In this paper we show that for any
convex Hamiltonian there exists a uniquely defined canonical global nonsmooth
coalescing flow that extends particle trajectories and determines dynamics
inside the shocks. We also provide a variational description of the
corresponding effective velocity field inside shocks, and discuss relation to
the "dissipative anomaly" in the limit of vanishing viscosity.Comment: 15 pages, no figures; to appear in Philos. Trans. R. Soc. series
Fatigue reliability method with in-service inspections
The first reliability method (FORM) has traditionally been applied in a fatigue reliability setting to one inspection interval at a time, so that the random distribution of crack lengths must be recharacterized following each inspection. The FORM presented here allow each analysis to span several inspection periods without explicit characterization of the crack length distribution upon each inspection. The method thereby preserves the attractive feature of FORM in that relatively few realizations in the random variable space need to be considered. Examples are given which show that the present methodology gives estimates which are in good agreement with Monte Carlo simulations and is efficient even for complex components
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