arXiv subjects

Hans Christian Öttinger

Publications and source records attributed to Hans Christian Öttinger.

At least 37 records · Page 2Linked to original sources

arXiv2018

GENERIC: Review of successful applications and a challenge for the future

We present and discuss the two-generator framework of nonequilibrium thermodynamics known as GENERIC ("general equation for the nonequilibrium reversible-irreversible coupling"), which is based on geometric concepts and on statistical mechanics. The usefulness and maturity of the framework are illustrated by reviewing a large number of successful applications. Finally, we offer an important challenge for the future. This abstract is based on the compact reviews [1;2] presenting modern nonequilibrium thermodynamics to applied scientists and engineers. In the spirit of a continuation of these reviews, we here add some new developments of the last five years.

cond-mat.soft↗

arXiv2018

Hamiltonian formulation of a class of constrained fourth-order differential equations in the Ostrogradsky framework

We consider a class of Lagrangians that depend not only on some configurational variables and their first time derivatives, but also on second time derivatives, thereby leading to fourth-order evolution equations. The proposed higher-order Lagrangians are obtained by expressing the variables of standard Lagrangians in terms of more basic variables and their time derivatives. The Hamiltonian formulation of the proposed class of models is obtained by means of the Ostrogradsky formalism. The structure of the Hamiltonians for this particular class of models is such that constraints can be introduced in a natural way, thus eliminating expected instabilities of the fourth-order evolution equations. Moreover, canonical quantization of the constrained equations can be achieved by means of Dirac's approach to generalized Hamiltonian dynamics.

math-ph↗

arXiv2018

Coarse-graining via the fluctuation-dissipation theorem and large-deviation theory

The fluctuation-dissipation theorem is a central result in statistical mechanics and is usually formulated for systems described by diffusion processes. In this paper, we propose a generalization for a wider class of stochastic processes, namely the class of Markov processes that satisfy detailed balance and a large-deviation principle. The generalized fluctuation-dissipation theorem characterizes the deterministic limit of such a Markov process as a generalized gradient flow, a mathematical tool to model a purely irreversible dynamics via a dissipation potential and an entropy function: these are expressed in terms of the large-deviation dynamic rate function of the Markov process and its stationary distribution. We exploit the generalized fluctuation-dissipation theorem to develop a new method of coarse-graining and test it in the context of the passage from the diffusion in a double-well potential to the jump process that describes the simple reaction $A \rightleftarrows B$ (Kramers' escape problem).

cond-mat.stat-mech↗

arXiv2018

Stability analysis for a thermodynamically consistent model of relativistic fluid dynamics

The search for thermodynamic admissibility moreover reveals a fundamental difference between liquids and gases in relativistic fluid dynamics, as the reversible convection mechanism is much simpler for liquids than for gases. In relativistic fluid mechanics, positive entropy production is known to be insufficient for guaranteeing stability. Much more restrictive criteria for thermodynamic admissibility have become available in nonequilibrium thermodynamics. We here perform a linear stability analysis for a model of relativistic hydrodynamics that is based on the GENERIC (general equation for the nonequilibrium reversible-irreversible coupling) framework of nonequilibrium thermodynamics. Assuming a simple form of the entropy function, we find stability for the entire range of physically meaningful model parameters. For relativistic fluid dynamics, full thermodynamic admissibility indeed leads to stability.

gr-qc↗

arXiv2018

Gravity as a Yang-Mills Theory Based on the Lorentz Group

The Yang-Mills theory associated with the restricted Lorentz group is revisited as a candidate for a theory of gravity. This is a natural idea because the principle of equivalence of gravitation and inertia suggests to introduce locally inertial coordinate systems with the gauge freedom of Lorentz transformations. Compared to previous implementations of the idea, we use a generalized expression for the vector potential of the gauge theory in terms of the metric, which involves a coupling constant. One can verify that, in the limit of small coupling constant, all the classical predictions of general relativity are reproduced. For the resulting higher-order field equations, the nature of the singularity associated with black holes changes. The proposed theory is based on a dimensionless action for coupling the Yang-Mills field to matter.

gr-qc↗

arXiv2018

BRST quantization of Yang-Mills theory: A purely Hamiltonian approach on Fock space

We develop the basic ideas and equations for the BRST quantization of Yang-Mills theories in an explicit Hamiltonian approach, without any reference to the Lagrangian approach at any stage of the development. We present a new representation of ghost fields that combines desirable self-adjointness properties with canonical anticommutation relations for ghost creation and annihilation operators, thus enabling us to characterize the physical states on a well-defined Fock space. The Hamiltonian is constructed by piecing together simple BRST invariant operators to obtain a minimal invariant extension of the free theory. It is verified that the evolution equations implied by the resulting minimal Hamiltonian provide a quantum version of the classical Yang-Mills equations. The modifications and requirements for the inclusion of matter are discussed in detail.

hep-th↗

arXiv2016

Quantum Field Theory as a Faithful Image of Nature

"All men by nature desire to know," states Aristotle in the famous first sentence of his Metaphysics. Knowledge about fundamental particles and interactions, that is, knowledge about the deepest aspects of matter, is certainly high if not top on the priority list, not only for physicists and philosophers. The goal of the present book is to contribute to this knowledge by going beyond the usual presentations of quantum field theory in physics textbooks, both in mathematical approach and by critical reflections inspired by epistemology, that is, by the branch of philosophy also referred to as the theory of knowledge. Hopefully, the present book motivates physicists to appreciate philosophical ideas. Epistemology and the philosophy of the evolution of science often seem to lag behind science and to describe the developments a posteriori. As philosophy here has a profound influence on the actual shaping of an image of fundamental particles and their interactions, our development should stimulate the curiosity and imagination of physicists. This book can be used as a textbook on quantum field theory for students of physics or as a monograph for philosophers and physicists interested in the epistemological foundations of particle physics. The benefits of an approach resting on philosophical foundations is twofold: the reader is stimulated to critical thinking and the entire story flows very naturally, thus removing all the mysteries from quantum field theory.

physics.hist-ph↗

arXiv2015

Biexponential decay and ultralong coherence of a single qubit

A quantum two-state system, weakly coupled to a heat bath, is traditionally studied in the Born-Markov regime under the secular approximation with completely positive linear master equations. Despite its success, this microscopic approach exclusively predicts exponential decays and Lorentzian susceptibility profiles, in disagreement with a number of experimental findings. To leave this limited paradigm, we use a phenomenological positive nonlinear master equation being both thermodynamically and statistically consistent. We find that, beyond a temperature-dependent threshold, a bifurcation in the decoherence time $T_2$ takes place; it gives rise to a biexponential decay and a susceptibility profile being neither Gaussian nor Lorentzian. This implies that, for suitable initial states, a major prolongation of the coherence can be obtained in agreement with recent experiments. Moreover, $T_2$ is no longer limited by the energy relaxation time $T_1$ offering novel perspectives to elaborate devices for quantum information processing.

quant-ph↗

arXiv2015

Modular Dynamical Semigroups for Quantum Dissipative Systems

We introduce a class of Markovian quantum master equations, able to describe the dissipative dynamics of a quantum system weakly coupled to one or several heat baths. The dissipative structure is driven by an entropic operator, the so called modular Hamiltonian, which makes it nonlinear. The generated Modular Dynamical Semigroup (MDS) is not, in general, a Quantum Dynamical Semigroup (QDS), whose dynamics is of the popular Lindblad type. The MDS has a robust thermodynamic structure, which guarantees for the positivity of the time evolved state, the correct steady state properties, the positivity of the entropy production, a positive Onsager matrix and Onsager symmetry relations (arising from Green-Kubo formulas). We show that the celebrated Davies generator, obtained through the Born and the secular approximations, generates a MDS. By unravelling the modular structure of the former, we provide a different and genuinely nonlinear MDS, not of QDS type, which is free from the severe spectral restrictions of the Davies generator, while still being supported by a weak coupling limit argument. With respect to the latter, the present work is a substantial extension of \cite{Ottinger2011_GEO,Ottinger2010_TLS_DHO}

quant-ph↗

arXiv2014

Numerics for Hyperbolic Conservation Laws with Help from the Physical Entropy

Stable numerical simulations for a hyperbolic system of conservation laws of relaxation type but not in divergence form are obtained by incorporating the physical entropy into the simulations. The entropy balance is utilized as an additional equation to eliminate the numerically critical terms with simple substitutions. The method has potential for a wider applicability than the particular example presented here.

math.NA↗

arXiv2014

Kinetic Theory and Stochastic Simulation of Field Quanta

We develop quantum electrodynamics into a kinetic-theory-like evolution equation for electrons, positrons and photons. To keep the "collision rules" simple, we make use of longitudinal and temporal photons in addition to the usual transverse photons. For our explicitly time-dependent approach, we introduce proper time-correlation functions. We then develop a stochastic simulation technique for solving the resulting kinetic equation and we comment on the subtleties associated with gauge invariance, Lorentz invariance and divergent integrals. To illustrate the validity and power of the proposed ideas, we show how a very simple simulation of the dynamics of field quanta can be used to obtain the main contribution to the anomalous magnetic moment of the electron.

hep-th↗

arXiv2012

Deformation of inherent structures to detect long-range correlations in supercooled liquids

We propose deformations of inherent structures as a suitable tool for detecting structural changes underlying the onset of cooperativity in supercooled liquids. The non-affine displacement (NAD) field resulting from the applied deformation shows characteristic differences between the high temperature liquid and supercooled state, that are typically observed in dynamic quantities. The average magnitude of the NAD is very sensitive to temperature changes in the supercooled regime and is found to be strongly correlated with the inherent structure energy. In addition, the NAD field is characterized by a correlation length that increases upon lowering the temperature towards the supercooled regime.

cond-mat.dis-nn↗

arXiv2011

Dynamic coarse-graining approach to quantum field theory

We build quantum field theory on the thermodynamic master equation for dissipative quantum systems. The vacuum is represented by a thermodynamic equilibrium state in the low-temperature limit. All regularization is consistently provided by a friction mechanism; with decreasing friction parameter, only degrees of freedom on shorter and shorter length scales are damped out of a quantum field theory. No divergent integrals need to be manipulated. Renormalization occurs as a tool to refine perturbation expansions, not to remove divergences. Relativistic covariance is recovered in the final results. We illustrate the proposed thermodynamic approach to quantum fields for the phi^4 theory by calculating the propagator and the beta function, and we offer some suggestions on its application to gauge theories.

math-ph↗

arXiv2010

Nonlinear thermodynamic quantum master equation: Properties and examples

The quantum master equation obtained from two different thermodynamic arguments is seriously nonlinear. We argue that, for quantum systems, nonlinearity occurs naturally in the step from reversible to irreversible equations and we analyze the nature and consequences of the nonlinear contribution. The thermodynamic nonlinearity naturally leads to canonical equilibrium solutions and extends the range of validity to lower temperatures. We discuss the Markovian character of the thermodynamic quantum master equation and introduce a solution strategy based on coupled evolution equations for the eigenstates and eigenvalues of the density matrix. The general ideas are illustrated for the two-level system and for the damped harmonic oscillator. Several conceptual implications of the nonlinearity of the thermodynamic quantum master equation are pointed out, including the absence of a Heisenberg picture and the resulting difficulties with defining multi-time correlations.

quant-ph↗

arXiv2010

Stochastic process behind nonlinear thermodynamic quantum master equation

We propose a piecewise deterministic Markovian jump process in Hilbert space such that the covariance matrix of this stochastic process solves the thermodynamic quantum master equation. The proposed stochastic process is particularly simple because the normalization of the vectors in Hilbert space is preserved only on average. As a consequence of the nonlinearity of the thermodynamic master equation, the construction of stochastic trajectories involves the density matrix as a running ensemble average. We identify a principle of detailed balance and a fluctuation-dissipation relation for our Markovian jump process.

quant-ph↗

arXiv2010

The nonlinear thermodynamic quantum master equation

The quantum master equation obtained by generalizing the geometric formulation of nonequilibrium thermodynamics to dissipative quantum systems is seriously nonlinear. We argue that nonlinearity occurs naturally in the step from reversible to irreversible equations and we analyze the nature of the nonlinear contribution. The thermodynamic nonlinearity leads to proper equilibrium solutions and improves the dynamic behavior of dissipative quantum systems. We also discuss the Markovian character of the thermodynamic quantum master equation. The general ideas are illustrated for two-level systems.

quant-ph↗

arXiv2010

The geometry and thermodynamics of dissipative quantum systems

Dirac's method of classical analogy is employed to incorporate quantum degrees of freedom into modern nonequilibrium thermodynamics. The proposed formulation of dissipative quantum mechanics builds entirely upon the geometric structures implied by commutators and canonical correlations. A lucid formulation of a nonlinear quantum master equation follows from the thermodynamic structure. Complex classical environments with internal structure can be handled readily.

quant-ph↗

arXiv2010

Lie groups in nonequilibrium thermodynamics: Geometric structure behind viscoplasticity

Poisson brackets provide the mathematical structure required to identify the reversible contribution to dynamic phenomena in nonequilibrium thermodynamics. This mathematical structure is deeply linked to Lie groups and their Lie algebras. From the characterization of all the Lie groups associated with a given Lie algebra as quotients of a universal covering group, we obtain a natural classification of rheological models based on the concept of discrete reference states and, in particular, we find a clear-cut and deep distinction between viscoplasticity and viscoelasticity. The abstract ideas are illustrated by a naive toy model of crystal viscoplasticity, but similar kinetic models are also used for modeling the viscoplastic behavior of glasses. We discuss some implications for coarse graining and statistical mechanics.

cond-mat.mtrl-sci↗