5,523 research outputs found
Transport theory yields renormalization group equations
We show that dissipative transport and renormalization can be described in a
single theoretical framework. The appropriate mathematical tool is the
Nakajima-Zwanzig projection technique. We illustrate our result in the case of
interacting quantum gases, where we use the Nakajima-Zwanzig approach to
investigate the renormalization group flow of the effective two-body
interaction.Comment: 11 pages REVTeX, twocolumn, no figures; revised version with
additional examples, to appear in Phys. Rev.
Lagrange formalism of memory circuit elements: classical and quantum formulations
The general Lagrange-Euler formalism for the three memory circuit elements,
namely, memristive, memcapacitive, and meminductive systems, is introduced. In
addition, {\it mutual meminductance}, i.e. mutual inductance with a state
depending on the past evolution of the system, is defined. The Lagrange-Euler
formalism for a general circuit network, the related work-energy theorem, and
the generalized Joule's first law are also obtained. Examples of this formalism
applied to specific circuits are provided, and the corresponding Hamiltonian
and its quantization for the case of non-dissipative elements are discussed.
The notion of {\it memory quanta}, the quantum excitations of the memory
degrees of freedom, is presented. Specific examples are used to show that the
coupling between these quanta and the well-known charge quanta can lead to a
splitting of degenerate levels and to other experimentally observable quantum
effects
The SLH framework for modeling quantum input-output networks
Many emerging quantum technologies demand precise engineering and control
over networks consisting of quantum mechanical degrees of freedom connected by
propagating electromagnetic fields, or quantum input-output networks. Here we
review recent progress in theory and experiment related to such quantum
input-output networks, with a focus on the SLH framework, a powerful modeling
framework for networked quantum systems that is naturally endowed with
properties such as modularity and hierarchy. We begin by explaining the
physical approximations required to represent any individual node of a network,
eg. atoms in cavity or a mechanical oscillator, and its coupling to quantum
fields by an operator triple . Then we explain how these nodes can be
composed into a network with arbitrary connectivity, including coherent
feedback channels, using algebraic rules, and how to derive the dynamics of
network components and output fields. The second part of the review discusses
several extensions to the basic SLH framework that expand its modeling
capabilities, and the prospects for modeling integrated implementations of
quantum input-output networks. In addition to summarizing major results and
recent literature, we discuss the potential applications and limitations of the
SLH framework and quantum input-output networks, with the intention of
providing context to a reader unfamiliar with the field.Comment: 60 pages, 14 figures. We are still interested in receiving
correction
Decoherent time-dependent transport beyond the Landauer-B\"uttiker formulation: a quantum-drift alternative to quantum jumps
We present a model for decoherence in time-dependent transport. It boils down
into a form of wave function that undergoes a smooth stochastic drift of the
phase in a local basis, the Quantum Drift (QD) model. This drift is nothing
else but a local energy fluctuation. Unlike Quantum Jumps (QJ) models, no jumps
are present in the density as the evolution is unitary. As a first application,
we address the transport through a resonant state
that undergoes decoherence. We show the equivalence with the decoherent steady
state transport in presence of a B\"{u}ttiker's voltage probe. In order to test
the dynamics, we consider two many-spin systems whith a local energy
fluctuation. A two-spin system is reduced to a two level system (TLS) that
oscillates among and . We show that QD model recovers not only
the exponential damping of the oscillations in the low perturbation regime, but
also the non-trivial bifurcation of the damping rates at a critical point, i.e.
the quantum dynamical phase transition. We also address the spin-wave like
dynamics of local polarization in a spin chain. The QD average solution has
about half the dispersion respect to the mean dynamics than QJ. By evaluating
the Loschmidt Echo (LE), we find that the pure states and are quite robust against the
local decoherence. In contrast, the LE, and hence coherence, decays faster when
the system is in a superposition state. Because its simple implementation, the
method is well suited to assess decoherent transport problems as well as to
include decoherence in both one-body and many-body dynamics.Comment: 10 pages, 5 figure
Best-fit quasi-equilibrium ensembles: a general approach to statistical closure of underresolved Hamiltonian dynamics
A new method of deriving reduced models of Hamiltonian dynamical systems is
developed using techniques from optimization and statistical estimation. Given
a set of resolved variables that define a model reduction, the
quasi-equilibrium ensembles associated with the resolved variables are employed
as a family of trial probability densities on phase space. The residual that
results from submitting these trial densities to the Liouville equation is
quantified by an ensemble-averaged cost function related to the information
loss rate of the reduction. From an initial nonequilibrium state, the
statistical state of the system at any later time is estimated by minimizing
the time integral of the cost function over paths of trial densities.
Statistical closure of the underresolved dynamics is obtained at the level of
the value function, which equals the optimal cost of reduction with respect to
the resolved variables, and the evolution of the estimated statistical state is
deduced from the Hamilton-Jacobi equation satisfied by the value function. In
the near-equilibrium regime, or under a local quadratic approximation in the
far-from-equilibrium regime, this best-fit closure is governed by a
differential equation for the estimated state vector coupled to a Riccati
differential equation for the Hessian matrix of the value function. Since
memory effects are not explicitly included in the trial densities, a single
adjustable parameter is introduced into the cost function to capture a
time-scale ratio between resolved and unresolved motions. Apart from this
parameter, the closed equations for the resolved variables are completely
determined by the underlying deterministic dynamics
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