arXiv subjects

Hans Christian Öttinger

Publications and source records attributed to Hans Christian Öttinger.

At least 19 recordsLinked to original sources

arXiv2026

From freely falling frames to the Lorentz gauge-symmetry group and a Hamiltonian composite theory of gravitation

The concept of freely falling frames suggests that gravity exhibits a local Lorentz gauge symmetry and requires a background Minkowski reference frame. The gauge vector fields of a Yang-Mills-type theory can be constructed from the transformations to these local freely falling frames, thereby leading to a composite theory of gravity. We propose coordinate conditions under which an exact black-hole solution can be obtained. Our analysis of planar gravitational waves reveals that, despite the large symmetry group, composite gravity possesses only four physical degrees of freedom. We elaborate a Hamiltonian formulation of composite gravity, derive the full set of constraints for the nonlinear theory, and outline the pathway toward its quantization.

gr-qc↗

arXiv2024

Comparative Analysis of Fluctuations in Viscoelastic Stress: A Comparison of the Temporary Network and Dumbbell models

Traditionally, stress fluctuations in flowing and deformed materials are overlooked, with an obvious focus on average stresses in a continuum mechanical approximation. However, these fluctuations, often dismissed as noise, hold the potential to provide direct insights into the material structure and its structure-stress coupling, uncovering detailed aspects of fluid transport and relaxation behaviors. Despite advancements in experimental techniques allowing for the visualization of these fluctuations, their significance remains largely untapped, as modeling efforts continue to target Newtonian fluids within the confines of Gaussian noise assumptions. In the present work a comparative analysis of stress fluctuations in two distinct microstructural models is carried out: the temporary network model and the dumbbell model. Despite both models conforming to the Upper Convected Maxwell Model at a macroscopic level, the temporary network model predicts non-Gaussian fluctuations. We find that stress fluctuations within the temporary network model exhibit more pronounced abruptness at local scale, with only an enlargement of the control volume leading to a gradual Gaussian-like noise, diminishing the differences between the two models. These findings underscore the heightened sensitivity of fluctuating rheology to microstructural details and the microstructure-flow coupling, beyond what is captured by macroscopically averaged stresses.

cond-mat.mtrl-sci↗

arXiv2024

Stochastic bra-ket interpretation of quantum mechanics

The stochastic nature of quantum mechanics is more naturally reflected in a bilinear two-process representation of density matrices rather than in squared wave functions. This proposition comes with a remarkable change of the entanglement mechanism: entanglement effects do not originate from superpositions of wave functions, but result from the bilinear structure of density matrices. Quantum interference appears as a multiplicative phenomenon rather than an additive superposition mechanism. We propose two general requirements such that the bilinear representation of density matrices is given in terms of two uniquely defined, identically distributed, Markovian stochastic jump processes. These general ideas are illustrated for the Einstein-Podolsky-Rosen and double-slit experiments. The expression of the stochastic nature of quantum mechanics in terms of random variables rather than their probability distributions facilitates an ontological viewpoint and leads us to a bra-ket interpretation of quantum mechanics.

quant-ph↗

arXiv2024

Elementary particles with nonzero spin must be massless

We present an ontological argument why elementary particles with nonzero spin must be massless. This argument implies that, from an ontological perspective, the massive quarks and leptons of the standard model cannot be elementary particles. This conclusion is less disquieting than it might seem at first sight because the Higgs mechanism entails that not only the masses of the W and Z bosons but also the masses of quarks and leptons arise from the interaction of massless elementary particles with the vacuum expectation value of the Higgs field, which is a result of symmetry breaking.

physics.gen-ph↗

arXiv2022

Quantum entanglement without superposition

Superposition states are at the origin of many paradoxes in quantum mechanics. By unraveling the von Neumann equation for density matrices, we develop a superposition-free formulation of quantum mechanics. Stochastic quantum jumps are a key feature of this approach, in blatant contrast with the continuity of the deterministic Schrödinger equation. We explain how quantum entanglement arises. Our superposition-free formulation results offers a new perspective on quantum mechanics.

quant-ph↗

arXiv2022

Conserved Currents for the Gauge-Field Theory with Lorentz Symmetry Group

For the Yang-Mills-type gauge-field theory with Lorentz symmetry group, we propose and verify an explicit expression for the conserved currents in terms of the energy-momentum tensor. A crucial ingredient is the assumption that the gauge symmetry arises from the decomposition of a metric in terms of tetrad variables. The currents exist under the weak condition that the energy-momentum tensor and the Ricci tensor commute. We show how the conserved currents can be used to obtain a composite theory of gravity and discuss the static isotropic field around a point mass at rest.

gr-qc↗

arXiv2022

Dissipation in spin chains using quantized nonequilibrium thermodynamics

We investigate the open dynamics of a chain of interacting spins using the quantized version of the GENERIC equation from classical out-of-equilibrium thermodynamics. We focus on both equilibrium and nonequilibrium scenarios for chains of different sizes. While in the equilibrium case we demonstrate thermal equilibration to the correct many-body Gibbs density matrix, in the nonequilibrium dynamics we show a ballistic-to-diffusive transition in the steady-state energy current and a scaling that is consistent with Fourier's law of heat transfer.

cond-mat.stat-mech↗

arXiv2022

Dynamical Triplet Unravelling: A quantum Monte Carlo algorithm for reversible dynamics

We introduce a quantum Monte Carlo method to simulate the reversible dynamics of correlated many-body systems. Our method is based on the Laplace transform of the time-evolution operator which, as opposed to most quantum Monte Carlo methods, makes it possible to access the dynamics at longer times. The Monte Carlo trajectories are realised through a piece-wise stochastic-deterministic reversible evolution where free dynamics is interspersed with two-process quantum jumps. The dynamical sign problem is bypassed via the so-called deadweight approximation, which stabilizes the many-body phases at longer times. We benchmark our method by simulating spin excitation propagation in the XXZ model and dynamical confinement in the quantum Ising chain, and show how to extract dynamical information from the Laplace representation.

quant-ph↗

arXiv2022

Fixed Point Quantum Monte Carlo

We present a new approach to the study of equilibrium properties in many-body quantum physics. Our method takes inspiration from Density Matrix Quantum Monte Carlo and incorporates new crucial features. First of all, the dynamics is transferred to the Laplace representation where an exact equation can be derived and solved using a simulation-step that, unlike most Monte Carlo methods, is not a priori physically bounded. Moreover, the spawning events are formulated in terms of two-process stochastic unravellings of quantum master equations, a formalism that is particularly useful when working with density matrices. And last, this is equivalent to an interaction picture, where the free part is integrated exactly and the convergence rate can be greatly increased if the interaction parameter is small. We benchmark our method by applying it to two case-studies in condensed matter physics, show its accuracy and further discuss its efficiency.

quant-ph↗

arXiv2021

A dynamically constrained Yang-Mills theory with Lorentz symmetry group as an alternative theory of gravity

We develop the complete composite theory of gravity, in which the gauge vector fields of the Yang-Mills theory with Lorentz symmetry group are expressed in terms of the tetrad variables obtained from the decomposition of a metric. A key element of a compelling formulation of composite gravity are refined coordinate conditions that offer a natural coupling of the gravitational field to matter and ensure the closest relationship to general relativity. The composite theory of gravity is presented from three different perspectives highlighting its intuitive interpretation, its relationship to general relativity and its canonical Hamiltonian formulation, where the latter clarifies the structure of the heavily constrained theory and provides the starting point for its quantization. The main physical ingredient of the theory is an anisotropic velocity-momentum relation, or tensorial mass, described by a metric. We discuss the static isotropic solution in great detail because it provides the background for the high-precision tests to be passed by an alternative theory of gravity and for the understanding of black holes.

gr-qc↗

arXiv2021

Coordinate conditions and field equations for pure composite gravity

Whenever an alternative theory of gravity is formulated in a background Minkowski space, the conditions characterizing admissible coordinate systems, in which the alternative theory of gravity may be applied, play an important role. We here propose Lorentz covariant coordinate conditions for the composite theory of pure gravity developed from the Yang-Mills theory based on the Lorentz group, thereby completing this previously proposed higher derivative theory of gravity. The physically relevant static isotropic solutions are determined by various methods, the high-precision predictions of general relativity are reproduced, and an exact black-hole solution with mildly singular behavior is found.

gr-qc↗

arXiv2020

The Dissipative Approach to Quantum Field Theory: Conceptual Foundations and Ontological Implications

Many attempts have been made to provide Quantum Field Theory with conceptually clear and mathematically rigorous foundations; remarkable examples are the Bohmian and the algebraic perspectives respectively. In this essay we introduce the dissipative approach to QFT, a new alternative formulation of the theory explaining the phenomena of particle creation and annihilation starting from nonequilibrium thermodynamics. It is shown that DQFT presents a rigorous mathematical structure, and a clear particle ontology, taking the best from the mentioned perspectives. Finally, after the discussion of its principal implications and consequences, we compare it with the main Bohmian QFTs implementing a particle ontology.

physics.hist-ph↗

arXiv2020

Mathematical structure and physical content of composite gravity in weak-field approximation

The natural constraints for the weak-field approximation to composite gravity, which is obtained by expressing the gauge vector fields of the Yang-Mills theory based on the Lorentz group in terms of tetrad variables and their derivatives, are analyzed in detail within a canonical Hamiltonian approach. Although this higher derivative theory involves a large number of fields, only few degrees of freedom are left, which are recognized as selected stable solutions of the underlying Yang-Mills theory. The constraint structure suggests a consistent double coupling of matter to both Yang-Mills and tetrad fields, which results in a selection among the solutions of the Yang-Mills theory in the presence of properly chosen conserved currents. Scalar and tensorial coupling mechanisms are proposed, where the latter mechanism essentially reproduces linearized general relativity. In the weak-field approximation, geodesic particle motion in static isotropic gravitational fields is found for both coupling mechanisms. An important issue is the proper Lorentz covariant criterion for choosing a background Minkowski system for the composite theory of gravity.

gr-qc↗

arXiv2020

A framework of nonequilibrium statistical mechanics. I. Role and type of fluctuations

Understanding the fluctuations by which phenomenological evolution equations with thermodynamic structure can be enhanced is the key to a general framework of nonequilibrium statistical mechanics. These fluctuations provide an idealized representation of microscopic details. We consider fluctuation-enhanced equations associated with Markov processes and elaborate the general recipes for evaluating dynamic material properties, which characterize force-flux constitutive laws, by statistical mechanics. Markov processes with continuous trajectories are conveniently characterized by stochastic differential equations and lead to Green-Kubo-type formulas for dynamic material properties. Markov processes with discontinuous jumps include transitions over energy barriers with the rates calculated by Kramers. We describe a unified approach to Markovian fluctuations and demonstrate how the appropriate type of fluctuations (continuous versus discontinuous) is reflected in the mathematical structure of the phenomenological equations.

cond-mat.stat-mech↗

arXiv2020

A framework of nonequilibrium statistical mechanics. II. Coarse-graining

For a given thermodynamic system, and a given choice of coarse-grained state variables, the knowledge of a force-flux constitutive law is the basis for any nonequilibrium modeling. In the first paper of this series we established how, by a generalization of the classical fluctuation-dissipation theorem (FDT), the structure of a constitutive law is directly related to the distribution of the fluctuations of the state variables. When these fluctuations can be expressed in terms of diffusion processes, one may use Green-Kubo-type coarse-graining schemes to find the constitutive laws. In this paper we propose a coarse-graining method that is valid when the fluctuations are described by means of general Markov processes, which include diffusions as a special case. We prove the success of the method by numerically computing the constitutive law for a simple chemical reaction $A \rightleftarrows B$. Furthermore, we show that one cannot find a consistent constitutive law by any Green-Kubo-like scheme.

cond-mat.stat-mech↗

arXiv2020

Structure-preserving integrators for dissipative systems based on reversible-irreversible splitting

We study the optimal design of numerical integrators for dissipative systems, for which there exists an underlying thermodynamic structure known as GENERIC (general equation for the nonequilibrium reversible-irreversible coupling). We present a frame-work to construct structure-preserving integrators by splitting the system into reversible and irreversible dynamics. The reversible part, which is often degenerate and reduces to a Hamiltonian form on its symplectic leaves, is solved by using a symplectic method (e.g., Verlet) with degenerate variables being left unchanged, for which an associated modified Hamiltonian (and subsequently a modified energy) in the form of a series expansion can be obtained by using backward error analysis. The modified energy is then used to construct a modified friction matrix associated with the irreversible part in such a way that a modified degeneracy condition is satisfied. The modified irreversible dynamics can be further solved by an explicit midpoint method if not exactly solvable. Our findings are verified by various numerical experiments, demonstrating the superiority of structure-preserving integrators over alternative schemes in terms of not only the accuracy control of both energy conservation and entropy production but also the preservation of the conformal symplectic structure in the case of linearly damped systems.

math.NA↗

arXiv2019

Natural Hamiltonian formulation of composite higher derivative theories

If a higher derivative theory arises from a transformation of variables that involves time derivatives, a tailor-made Hamiltonian formulation is shown to exist. The details and advantages of this elegant Hamiltonian formulation, which differs from the usual Ostrogradsky approach to higher derivative theories, are elaborated for mechanical systems and illustrated for simple examples. Both a canonical space and a set of constraints emerge naturally from the transformation rule for the variables. In other words, the setting for quantization and the procedure for eliminating instabilities arise naturally.

math-ph↗

arXiv2019

An Alternative to the Lagrangian and Hamiltonian Formulations of Relativistic Field Theories Based on the Energy-Momentum Tensor

A Noether-enhanced Legendre transformation from Lagrange densities to energy-momentum tensors is developed into an alternative framework for formulating classical field equations. This approach offers direct access to the Hamiltonian while keeping manifest Lorentz covariance in the formulation of relativistic field theories. The field equations are obtained by imposing a vanishing divergence of the energy-momentum tensor (in a suitably structured form). The proposed framework is ideally suited for coupling subsystems because their interaction can be expressed as an exchange of energy and momentum. Even higher derivative theories and dissipative systems can be treated. A most promising application is the formulation of alternative theories of gravity. The proposed framework is illustrated for Yang-Mills theories, for which it offers a covariant canonical quantization scheme.

physics.gen-ph↗