1,679 research outputs found
Finite-time thermodynamics of port-Hamiltonian systems
In this paper, we identify a class of time-varying port-Hamiltonian systems
that is suitable for studying problems at the intersection of statistical
mechanics and control of physical systems. Those port-Hamiltonian systems are
able to modify their internal structure as well as their interconnection with
the environment over time. The framework allows us to prove the First and
Second laws of thermodynamics, but also lets us apply results from optimal and
stochastic control theory to physical systems. In particular, we show how to
use linear control theory to optimally extract work from a single heat source
over a finite time interval in the manner of Maxwell's demon. Furthermore, the
optimal controller is a time-varying port-Hamiltonian system, which can be
physically implemented as a variable linear capacitor and transformer. We also
use the theory to design a heat engine operating between two heat sources in
finite-time Carnot-like cycles of maximum power, and we compare those two heat
engines.Comment: To appear in Physica D (accepted July 2013
Effective Quantum Theories for Transport in Inhomogeneous Systems with Non-trivial Band Structure
Starting from a general -band Hamiltonian with weak spatial and temporal
variations, we derive a low energy effective theory for transport within one or
several overlapping bands. To this end, we use the Wigner representation that
allows us to systematically construct the unitary transformation that brings
the Hamiltonian into band-diagonal form. We address the issue of gauge
invariance and discuss the necessity of using kinetic variables in order to
obtain a low energy effective description that is consistent with the original
theory. Essentially, our analysis is a semiclassical one and quantum
corrections appear as Berry curvatures in addition to quantities that are
related to the appearance of persistent currents. We develop a transport
framework which is manifestly gauge invariant and it is based on a quantum
Boltzman formulation along with suitable definitions of current density
operators such that Liouville's theorem is satisfied. Finally, we incorporate
the effects of an external electromagnetic field into our theory.Comment: 22 pages, 2 figure
From canonical Hamiltonian to Port-Hamiltonian modeling application to magnetic shape memory alloys actuators.
International audienceThis paper presents the modelling of an actuator based on Magnetic Shape Memory Alloys (MSMA). The actuation principle relies on the ability of the material to change its shape under the application of a magnetic field. Previous models proposed by authors were based on canonical (symplectic) Hamiltonian modeling and thermodynamics of irreversible processes. These models, though physically cogent, are non-minimal differential algebraic dynamical models and hence less adapted for control purposes.This paper therefore proposes a modified and systemoriented modeling procedure which lends itself naturally to a port-Hamiltonian model. The latter is found to be a minimal realization of the above whereby interconnection between subsystems is clearly visible. Using Lagrange multipliers, constraints which arise due to causality and interconnection are expressed. In the last section, Differential Algebraic Equations (DAE) resulting from previous models are reduced to Ordinary Differential Equations (ODE) and by using coordinate transformations, constraints are decoupled from the system input/output. The resulting model is well-suited for control
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
Hamilton--Jacobi theory for continuation of magnetic field across a toroidal surface supporting a plasma pressure discontinuity
The vanishing of the divergence of the total stress tensor (magnetic plus
kinetic) in a neighborhood of an equilibrium plasma containing a toroidal
surface of discontinuity gives boundary and jump conditions that strongly
constrain allowable continuations of the magnetic field across the surface. The
boundary conditions allow the magnetic fields on either side of the
discontinuity surface to be described by surface magnetic potentials, reducing
the continuation problem to that of solving a Hamilton--Jacobi equation. The
characteristics of this equation obey Hamiltonian equations of motion, and a
necessary condition for the existence of a continued field across a general
toroidal surface is that there exist invariant tori in the phase space of this
Hamiltonian system. It is argued from the Birkhoff theorem that existence of
such an invariant torus is also, in general, sufficient for continuation to be
possible. An important corollary is that the rotational transform of the
continued field on a surface of discontinuity must, generically, be irrational.Comment: Prepared for submission to Phys. Letts.
Berry Phase Effects on Electronic Properties
Ever since its discovery, the Berry phase has permeated through all branches
of physics. Over the last three decades, it was gradually realized that the
Berry phase of the electronic wave function can have a profound effect on
material properties and is responsible for a spectrum of phenomena, such as
ferroelectricity, orbital magnetism, various (quantum/anomalous/spin) Hall
effects, and quantum charge pumping. This progress is summarized in a
pedagogical manner in this review. We start with a brief summary of necessary
background, followed by a detailed discussion of the Berry phase effect in a
variety of solid state applications. A common thread of the review is the
semiclassical formulation of electron dynamics, which is a versatile tool in
the study of electron dynamics in the presence of electromagnetic fields and
more general perturbations. Finally, we demonstrate a re-quantization method
that converts a semiclassical theory to an effective quantum theory. It is
clear that the Berry phase should be added as a basic ingredient to our
understanding of basic material properties.Comment: 48 pages, 16 figures, submitted to RM
Relativistic quantum measurement
Does the measurement of a quantum system necessarily break Lorentz
invariance? We present a simple model of a detector that measures the spacetime
localization of a relativistic particle in a Lorentz invariant manner. The
detector does not select a preferred Lorentz frame as a Newton-Wigner
measurement would do. The result indicates that there exists a Lorentz
invariant notion of quantum measurement and sheds light on the issue of the
localization of a relativistic particle. The framework considered is that of
single-particle mechanics as opposed to field theory. The result may be taken
as support for the interpretation postulate of the spacetime-states formulation
of single-particle quantum theory.Comment: 9 pages, no figures: Revision: references adde
Proposal for an Optomechanical Traveling Wave Phonon-Photon Translator
In this article we describe a general optomechanical system for converting
photons to phonons in an efficient, and reversible manner. We analyze
classically and quantum mechanically the conversion process and proceed to a
more concrete description of a phonon-photon translator formed from coupled
photonic and phononic crystal planar circuits. Applications of the
phonon-photon translator to RF-microwave photonics and circuit QED, including
proposals utilizing this system for optical wavelength conversion, long-lived
quantum memory and state transfer from optical to superconducting qubits are
considered.Comment: 32 pages, 11 figure
Irreversible port-Hamiltonian systems : a general formulation of irreversible processes with application to the CSTR.
International audienceIn this paper we suggest a class of quasi-port Hamiltonian systems called Irreversible port Hamiltonian Systems, that expresses simultaneously the first and second principle of thermodynamics as a structural property. These quasi-port Hamiltonian systems are defined with respect to a structure matrix and a modulating function which depends on the thermodynamic relation between state and co-state variables of the system. This modulating function itself is the product of some positive function and the Poisson bracket of the entropy and the energy function. This construction guarantees that the Hamiltonian function is a conserved quantity and simultaneously that the entropy function satisfies a balance equation containing an irreversible entropy creation term. In the second part of the paper, we suggest a lift of the Irreversible Port Hamiltonian Systems to control contact systems defined on the Thermodynamic Phase Space which is canonically endowed with a contact structure associated with Gibbs' relation. For this class of systems we have suggested a lift which avoids any singularity of the contact Hamiltonian function and defines a control contact system on the complete Thermodynamic Phase Space, in contrast to the previously suggested lifts of such systems. Finally we derive the formulation of the balance equations of a CSTR model as an Irreversible Port Hamiltonian System and give two alternative lifts of the CSTR model to a control contact system defined on the complete Thermodynamic Phase Space
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