arXiv subjects

Matthias Schmidt

Publications and source records attributed to Matthias Schmidt.

At least 73 records · Page 4Linked to original sources

arXiv2020

Deformation quantization and homological reduction of a lattice gauge model

For a compact Lie group $G$ we consider a lattice gauge model given by the $G$-Hamiltonian system which consists of the cotangent bundle of a power of $G$ with its canonical symplectic structure and standard moment map. We explicitly construct a Fedosov quantization of the underlying symplectic manifold using the Levi-Civita connection of the Killing metric on $G$. We then explain and refine quantized homological reduction for the construction of a star product on the symplectically reduced space in the singular case. Afterwards we show that for $G = \operatorname{SU} (2)$ the main hypotheses ensuring the method of quantized homological reduction to be applicable hold in the case of our lattice gauge model. For that case, this implies that the - in general singular - symplectically reduced phase space of the corresponding lattice gauge model carries a star product.

math-ph↗

arXiv2020

Flow and structure in nonequilibrium Brownian many-body systems

We present a fundamental classification of forces relevant in nonequilibrium structure formation under collective flow in Brownian many-body systems. The internal one-body force field is systematically split into contributions relevant for the spatial structure and for the coupled motion. We demonstrate that both contributions can be obtained straightforwardly in computer simulations, and present a power functional theory that describes all types of forces quantitatively. Our conclusions and methods are relevant for flow in inertial systems, such as molecular liquids and granular media.

cond-mat.soft↗

arXiv2020

Active interface polarization is a state function

We prove three exact sum rules that relate the polarization of active Brownian particles to their one-body current: (i) The total polarization vanishes, provided that there is no net flux through the boundaries, (ii) at any planar wall the polarization is determined by the magnitude of the bulk current, and (iii) the total interface polarization between phase-separated fluid states is rigorously determined by the gas-liquid current difference. This result precludes the influence of the total interface polarization on active bulk coexistence and questions the proposed coupling of interface to bulk.

cond-mat.stat-mech↗

arXiv2020

Non-negative Interfacial Tension in Phase-Separated Active Brownian Particles

We present a microscopic theory for the nonequilibrium interfacial tension $γ_{\rm gl}$ of the free interface between gas and liquid phases of active Brownian particles. The underlying square gradient treatment and the splitting of the force balance in flow and structural contributions is general and applies to inhomogeneous nonequilibrium steady states. We find $γ_{\rm gl}\geq 0$, which opposes claims by Bialké et al. [Phys. Rev. Lett. $\bf{115}$, 098301 (2015)] and delivers the theoretical justification for the widely observed interfacial stability in active Brownian dynamics many-body simulations.

cond-mat.stat-mech↗

arXiv2020

Stratified structure of the observable algebra of Hamiltonian lattice gauge theory

We consider Kaehler quantized models whose underlying classical phase space has a stratified structure induced from the Hamiltonian action of a compact Lie group. We show how to implement the classical stratification on the level of the C*-algebra of observables and discuss the relation to the costratification (in the sense of Huebschmann) of the physical Hilbert space. Our analysis is based on the T-procedure as developed by Grundling and Hurst. We apply the general theory to Yang-Mills theory on a finite lattice, where the stratification is given by the classical gauge orbit types.

math-ph↗

arXiv2019

Phase coexistence of active Brownian particles

We investigate motility-induced phase separation of active Brownian particles, which are modeled as purely repulsive spheres that move due to a constant swim force with freely diffusing orientation. We develop on the basis of power functional concepts an analytical theory for nonequilibrium phase coexistence and interfacial structure. Theoretical predictions are validated against Brownian dynamics computer simulations. We show that the internal one-body force field has four nonequilibrium contributions: (i) isotropic drag and (ii) interfacial drag forces against the forward motion, (iii) a superadiabatic spherical pressure gradient and (iv) the quiet life gradient force. The intrinsic spherical pressure is balanced by the swim pressure, which arises from the polarization of the free interface. The quiet life force opposes the adiabatic force, which is due to the inhomogeneous density distribution. The balance of quiet life and adiabatic forces determines bulk coexistence via equality of two bulk state functions, which are independent of interfacial contributions. The internal force fields are kinematic functionals which depend on density and current, but are independent of external and swim forces, consistent with power functional theory. The phase transition originates from nonequilibrium repulsion, with the agile gas being more repulsive than the quiet liquid.

cond-mat.stat-mech↗

arXiv2019

Memory-induced motion reversal in Brownian liquids

We study the Brownian dynamics of hard spheres under spatially inhomogeneous shear, using event-driven Brownian dynamics simulations and power functional theory. We examine density and current profiles both for steady states and for the transient dynamics after switching on and switching off an external square wave shear force field. We find that a dense hard sphere fluid (volume fraction $\approx$0.35) undergoes global motion reversal after switching off the shear force field. We use power functional theory with a spatially nonlocal memory kernel to describe the superadiabatic force contributions and obtain good quantitative agreement of the theoretical results with simulation data. The theory provides an explanation for the motion reversal: Internal superadiabatic nonequilibrium forces that oppose the externally driven current arise due to memory after switching off. The effect is genuinely viscoelastic: in steady state, viscous forces oppose the current, but they elastically generate an opposing current after switch-off.

cond-mat.soft↗

arXiv2019

Lifetimes and g-factors of the HFS states in H-like and Li-like bismuth

The LIBELLE experiment performed at the experimental storage ring (ESR) at the GSI Helmholtz Center for Heavy Ion Research in Darmstadt, Germany, has successfully determined the ground state hyperfine (HFS) splittings in hydrogen-like ($^{209}\rm{Bi}^{82+}$) and lithium-like ($^{209}\rm{Bi}^{80+}$) bismuth. The study of HFS transitions in highly charged ions enables precision tests of QED in extreme electric and magnetic fields otherwise not attainable in laboratory experiments. Besides the transition wavelengths the time resolved detection of fluorescence photons following the excitation of the ions by a pulsed laser system also allows to extract lifetimes of the upper HFS levels and g-factors of the bound 1s and 2s electrons for both charge states. While the lifetime of the upper HFS state in $^{209}\rm{Bi}^{82+}$ has already been measured in earlier experiments, an experimental value for lifetime of this state in $^{209}\rm{Bi}^{80+}$ is reported for the first time in this work.

physics.atom-ph↗

arXiv2018

Custom flow in overdamped Brownian Dynamics

When an external field drives a colloidal system out of equilibrium, the ensuing colloidal response can be very complex and obtaining a detailed physical understanding often requires case-by-case considerations. In order to facilitate systematic analysis, here we present a general iterative scheme for the determination of the unique external force field that yields a prescribed inhomogeneous stationary or time-dependent flow in an overdamped Brownian many-body system. The computer simulation method is based on the exact one-body force balance equation and allows to specifically tailor both gradient and rotational velocity contributions, as well as to freely control the one-body density distribution. Hence compressibility of the flow field can be fully adjusted. The practical convergence to a unique external force field demonstrates the existence of a functional map from both velocity and density to external force field, as predicted by the power functional variational framework. In equilibrium, the method allows to find the conservative force field that generates a prescribed target density profile, and hence implements the Mermin-Evans classical density functional map from density distribution to external potential. The conceptual tools developed here enable one to gain detailed physical insight into complex flow behaviour, as we demonstrate in prototypical situations.

cond-mat.soft↗

arXiv2018

Better than counting: Density profiles from force sampling

Calculating one-body density profiles in equilibrium via particle-based simulation methods involves counting of events of particle occurrences at (histogram-resolved) space points. Here we investigate an alternative method based on a histogram of the local force density. Via an exact sum rule the density profile is obtained with a simple spatial integration. The method circumvents the inherent ideal gas fluctuations. We have tested the method in Monte Carlo, Brownian Dynamics and Molecular Dynamics simulations. The results carry a statistical uncertainty smaller than that of the standard, counting, method, reducing therefore the computation time.

cond-mat.soft↗

arXiv2018

Structural nonequilibrium forces in driven colloidal systems

We identify a structural one-body force field that sustains spatial inhomogeneities in nonequilibrium overdamped Brownian many-body systems. The structural force is perpendicular to the local flow direction, it is free of viscous dissipation, it is microscopically resolved in both space and and time, and it can stabilize density gradients. From the time evolution in the exact (Smoluchowski) low-density limit, Brownian dynamics simulations and a novel power functional approximation, we obtain a quantitative understanding of viscous and structural forces, including memory and shear migration.

cond-mat.soft↗

arXiv2018

The Hilbert space costratification for the orbit type strata of SU(2)-lattice gauge theory

We construct the Hilbert space costratification of $G=\mathrm{SU}(2)$-quantum gauge theory on a finite spatial lattice in the Hamiltonian approach. We build on previous work where we have implemented the classical gauge orbit strata on quantum level within a suitable holomorphic picture. In this picture, each element $τ$ of the classical stratification corresponds to the zero locus of a finite subset $\{p_i\}$ of the algebra $\mathcal R$ of $G$-invariant representative functions on the complexification of $G^N$. Viewing the invariants as multiplication operators $\hat p_i$ on the Hilbert space $\mathcal H$, the union of their images defines a subspace of $\mathcal H$ whose orthogonal complement $\mathcal H_τ$ is the element of the costratification corresponding to $τ$. To construct $\mathcal H_τ$, one has to determine the images of the $\hat p_i$ explicitly. To accomplish that goal, we construct an orthonormal basis in $\mathcal H$ and determine the multiplication law for the basis elements, that is, we determine the structure constants of $\mathcal R$ in this basis. This part of our analysis applies to any compact Lie group $G$. For $G = \mathrm{SU}(2)$, the above procedure boils down to a problem in combinatorics of angular momentum theory. Using this theory, we obtain the union of the images of the operators $\hat p_i$ as a subspace generated by vectors whose coefficients with respect to our basis are given in terms of Wigner's $3nj$ symbols. The latter are further expressed in terms of $9j$ symbols. Using these techniques, we are also able to reduce the eigenvalue problem for the Hamiltonian of this theory to a problem in linear algebra.

math-ph↗

arXiv2017

Active ideal sedimentation: Exact two-dimensional steady states

We consider an ideal gas of active Brownian particles that undergo self-propelled motion and both translational and rotational diffusion under the influence of gravity. We solve analytically the corresponding Smoluchowski equation in two space dimensions for steady states. The resulting one-body density is given as a series, where each term is a product of an orientation-dependent Mathieu function and a height-dependent exponential. A lower hard wall is implemented as a no-flux boundary condition. Numerical evaluation of the suitably truncated analytical solution shows the formation of two different spatial regimes upon increasing Peclet number. These regimes differ in their mean particle orientation and in their variation of the orientation-averaged density with height.

cond-mat.soft↗

arXiv2017

Velocity gradient power functional for Brownian dynamics

We present an explicit and simple approximation for the superadiabatic excess (over ideal gas) free power functional, admitting the study of the nonequilibrium dynamics of overdamped Brownian many-body systems. The functional depends on the local velocity gradient and is systematically obtained from treating the microscopic stress distribution as a conjugate field. The resulting superadiabatic forces are beyond dynamical density functional theory and are of viscous nature. Their high accuracy is demonstrated by comparison to simulation results.

cond-mat.soft↗

arXiv2017

Defining relations for the orbit type strata of SU(2)-lattice gauge models

We consider an SU(2)-lattice gauge model in the tree gauge. Classically, this is a system with symmetries whose configuration space is a direct product of copies of SU(2), acted upon by diagonal inner automorphisms. We derive defining relations for the orbit type strata in the reduced classical phase space. The latter is realized as a certain quotient of a direct product of copies of the complexified group SL(2,\CC) (sometimes named the GIT-quotient because it provides a categorical quotient in the sense of geometric invariant theory). The relations derived can be used for the construction of the orbit type costratification of the Hilbert space of the quantum system in the sense of Huebschmann.

math-ph↗

arXiv2016

Nonequilibrium phase behaviour from minimization of free power dissipation

We develop a general theory for describing phase coexistence between nonequilibrium steady states in Brownian systems, based on power functional theory (M. Schmidt and J.M. Brader, J. Chem. Phys. 138, 214101 (2013)). We apply the framework to the special case of fluid-fluid phase separation of active soft sphere swimmers. The central object of the theory, the dissipated free power, is calculated via computer simulations and compared to a simple analytical approximation. The theory describes well the simulation data and predicts motility-induced phase separation due to avoidance of dissipative clusters.

cond-mat.soft↗

arXiv2016

Superadiabatic forces in the dynamics of the one-dimensional Gaussian core model

Using Brownian dynamics computer simulations we investigate the dynamics of the one-body density and one-body current in a one-dimensional system of particles that interact with a repulsive Gaussian pair potential. We systematically split the internal force distribution into an adiabatic part, which originates from the equilibrium free energy, and a superadiabatic contribution, which is neglected in dynamical density functional theory. We find a strong dependence of the magnitude and phase of the superadiabatic force distribution on the initial state of the system. While the magnitude of the superadiabatic force is small if the system evolves from an equilibrium state inside of a parabolic external potential, it is large for particles with equidistant initial separations at high temperature. We analyze these findings in the light of the known mean-field behavior of Gaussian core particles and discuss a multi-occupancy mechanism which generates superadiabatic forces that are out of phase with respect to the adiabatic force.

cond-mat.soft↗

arXiv2016

Assembly of open clusters of colloidal dumbbells via droplet evaporation

We investigate the behavior of a mixture of asymmetric colloidal dumbbells and emulsion droplets by means of kinetic Monte Carlo simulations. The evaporation of the droplets and the competition between droplet-colloid attraction and colloid-colloid interactions leads to the formation of clusters built up of colloid aggregates with both closed and open structures. We find that stable packings and hence complex colloidal structures can be obtained by changing the relative size of the colloidal spheres and/or their interfacial tension with the droplets.

cond-mat.soft↗