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Geoffrey L. Sewell

Publications and source records attributed to Geoffrey L. Sewell.

12 recordsLinked to original sources
arXiv2020

W*-Dynamics of Infinite Dissipative Quantum Systems

We formulate the dynamics of an infinitely extended open dissipative quantum system, ${Σ]$,in the Schroedinger picture.The generic model on which this is based comprises a C*-algebra,$[\cal A}$,of observables, a folium, ${\cal F}$, of states on this algebra and a one parameter semigroup,$τ$, of linear transformations of ${\cal F}$ that represents its dynamics and is given by a natural infinite volume limit of the corresponding semigroup for a finite system. On this basis, we establish that the dynamic of $Σ$ is given by a one parameter semigroup of completely positive transformations of the W*-star algebra dual to ${\cal F}$. This result serves to extend our earlier formulation [1[ of infinitely extended conservative systems to open dissipative ones.

math-ph↗
arXiv2015

Model of Antiferromagnetic Superconductivity

We present a simple model that supports superconductive and antiferromagnetic ordering. The model consists of a system of electrons on a simple cubic lattice that move by tunnel effect and interact via antiferromagnetic Ising spin couplings and short range repulsions: these include infinitely strong Hubbard forces that prevent double occupancy of any lattice site. Hence, under the filling condition of one electron per site and at sufficiently low temperature, the system is an antiferromagnetic Mott insulator. However, when holes are created by suitable doping, they are mobile charge carriers. We show that, at low concentration, their interactions induced by the above interelectronic ones lead to Schafroth pairing. Hence, under certain plausible but unproved assumptions, the model exhibits the off-diagonal long range order that characterises superconductivity, while retaining the antiferromagnetic ordering.

cond-mat.supr-con↗
arXiv2015

Hyperbolic Flows and the Question of Quantum Chaos

Hyperbolic flows, as formulated by Anosov, are the prototypes of chaotic evolutions in classical dynamical systems. Here we provide a concise updated account of their quantum counterparts originally formulated by Emch, Narnhofer, Thirring and Sewell within the operator algebraic setting of quantum theory: and we discuss their bearing on the question of quantum chaos.

math-ph↗
arXiv2013

Local Thermodynamic Equilibrium at Three Levels

We present coordinated formulations of local thermodynamical equilibrium conditions at three levels, namely the macroscopic one of classical thermodynamics, the mesoscopic one of hydrodynamical fluctuations and the microscopic one of quantum statistical mechanics. These conditions are all expressed in terms of the hydrodynamical variables of the macroscopic picture, and the quantum statistical ones are shown to imply a local version of the zeroth law.

math-ph↗
arXiv2012

Macrostatistics and Fluctuating Hydrodynamics

We extend our earlier macrostatistical treatment of hydrodynamical fluctuations about nonequilibrium steady states to viscous fluids. Since the scale dependence of the Navier-Stokes equations precludes the applicability of any infinite scale (hydrodynamical) limit, this has to be based on the generic model of a large but finite system, rather than an infinite one. On this basis, together with assumptions of Onsager's regression hypothesis and conditions of local equilibrium and chaoticity, we show that the hydrodynamical fluctuations of a reservoir driven fluid about a nonequilibrium steady state execute a Gaussian Markov process that constitutes a mathematical structure for a generalised version of Landau's fluctuating hydrodynamics and generically carries long range spatial correlations.

math-ph↗
arXiv2010

Note on the Relativistic Thermodynamics of Moving Bodies

We employ a novel thermodynamical argument to show that, at the macroscopic level,there is no intrinsic law of temperature transformation under Lorentz boosts. This result extends the corresponding microstatistical one of earlier works to the purely macroscopic regime and signifies that the concept of temperature as an objective entity is restricted to the description of bodies in their rest frames. The argument on which this result is based is centred on the thermal transactions between a body that moves with uniform velocity relative to a certain inertial frame and a thermometer, designed to measure its temperature, that is held at rest in that frame.

math-ph↗
arXiv2009

Statistical Thermodynamics of Moving Bodies

We resolve the long standing question of temperature dependence of uniformly moving bodies by means of a quantum statistical treatment centred on the zeroth law of thermodynamics. The key to our treatment is the result, established by Kossakowski et al, that a macroscopic body behaves as a thermal reservoir with well-defined temperature, in the sense of the zeroth law, if and only if its state satisfies the Kubo-Martin-Schwinger (KMS) condition. In order to relate this result to the relativistic thermodynamics of moving bodies, we employ the Tomita-Takesaki modular theory to prove that a state cannot satisfy the KMS conditions with respect to two different inertial frames whose relative velocity is non-zero. This implies that the concept of temperature stemming from the zeroth law is restricted to states of bodies in their rest frames and thus that there is no law of temperature transformations under Lorentz boosts. The corresponding results for nonrelativistic Galilean systems have also been established.

math-ph↗
arXiv2008

On the Mathematical Theory of Superfluidity

We provide a general operator algebraic formulation of superfluidity in Bose systems, with the aim of investigating the relationships of this phenomenon both to off-diagonal long range order (ODLRO) and to a mathematically precise version of Landau's picture of elementary excitations. Our principal results are that ODLRO leads both to rotational superfluidity and to Goldstone excitations, while the neo-Landau picture accounts for the translational superfluidity of flow along a pipe. The latter picture is realised by the Lieb-Liniger-Girardeau model. Open problems are briefly discussed.

math-ph↗
arXiv2008

On the Question of Temperature Transformations under Lorentz and Galilei Boosts

We provide a quantum statistical thermodynamical solution of the long standing problem of temperature transformations of uniformly moving bodies. Our treatment of this question is based on the well established quantum statistical result that the thermal equilibrium conditions demanded by both the Zeroth and Second Laws of Thermodynamics are precisely those of Kubo, Martin and Schwinger (KMS). We prove that, in both the special relativistic and nonrelativistic settings, a state of a body cannot satisfy these conditions for different inertial frames with non-zero relative velocity. Hence a body that serves as a thermal reservoir, in the sense of the Zeroth Law, in an inertial rest frame cannot do so in a laboratory frame relative to which it moves with non-zero uniform velocity. Consequently, there is no law of temperature transformation under either Lorentz or Galilei boosts, and so the concept of temperature stemming from the Zeroth Law is restricted to states of bodies in their rest frames.

math-ph↗
arXiv2005

Quantum Macrostatistical Theory of Nonequilibrium Steady States

We provide a general macrostatistical formulation of nonequilibrium steady states of reservoir driven quantum systems. This formulation is centred on the large scale properties of the locally conserved hydrodynamical observables, and our basic assumptions comprise (a) a chaoticity hypothesis for the nonconserved currents carried by these observables, (b) an extension of Onsager's regression hypothesis to the fluctuations about nonequilibrium states, and (c) a certain mesoscopic local equilibrium hypothesis. On this basis we obtain a picture wherein the fluctuations of the hydrodynamical observables about a nonequilibrium steady state execute a Gaussian Markov process of a generalized Onsager-Machlup type, which is completely determined by the position dependent transport coefficients and the equilibrium entropy function of the system. This picture reveals that the transport coefficients satisfy a generalized form of the Onsager reciprocity relations in the nonequilibrium situation and that the spatial correlations of the hydrodynamical observables are generically of long range. This last result constitutes a model-independent generalization of that obtained for special classical stochastic systems and marks a striking difference between the steady nonequilibrium and equilibrium states, since it is only at critical points that the latter carry long range correlations.

math-ph↗
arXiv2004

Quantum macrostatistical picture of nonequilibrium steady states

We employ a quantum macrostatistical treatment of irreversible processes to prove that, in nonequilibrium steady states, (a) the hydrodynamical observables execute a generalised Onsager-Machlup process and (b) the spatial correlations of these observables are generically of long range. The key assumptions behind these results are a nonequilibrium version of Onsager's regression hypothesis, together with certain hypotheses of chaoticity and local equilibrium for hydrodynamical fluctuations.

math-ph↗