arXiv subjects

Rudolf Haussmann

Publications and source records attributed to Rudolf Haussmann.

10 recordsLinked to original sources

arXiv2022

Continuum mechanics for the elastic properties of crystals: Microscopic approach based on projection-operator formalism

We present a microscopic derivation of the laws of continuum mechanics of nonideal ordered solids including dissipation, defect diffusion, and heat transport. Starting point is the classical many-body Hamiltonian. The approach relies on the Zwanzig-Mori projection operator formalism to connect microscopic fluctuations to thermodynamic derivatives and transport coefficients. Conservation laws and spontaneous symmetry breaking, implemented via Bogoliubov's inequality, determine the selection of the slow variables. Density fluctuations in reciprocal space encode the displacement field and the defect concentration. Isothermal and adiabatic elastic constants are obtained from equilibrium correlations, while transport coefficients are given as Green-Kubo formulae, providing the basis for their measurement in atomistic simulations or colloidal experiments. The approach and results are compared to others from the literature.

cond-mat.stat-mech↗

arXiv2022

Microscopic density-functional approach to nonlinear elasticity theory

Starting from a general classical model of many interacting particles we present a well defined step by step procedure to derive the continuum-mechanics equations of nonlinear elasticity theory with fluctuations which describe the macroscopic phenomena of a solid crystal. As the relevant variables we specify the coarse-grained densities of the conserved quantities and a properly defined displacement field which describes the local translations, rotations, and deformations. In order to stay within the framework of the conventional density-functional theory we first and mainly consider the isothermal case and omit the effects of heat transport and warming by friction where later we extend our theory to the general case and include these effects. We proceed in two steps. First, we apply the concept of local thermodynamic equilibrium and minimize the free energy functional under the constraints that the macroscopic relevant variables are fixed. As results we obtain the local free energy density and we derive explicit formulas for the elastic constants which are exact within the framework of density-functional theory. Second, we apply the methods of nonequilibrium statistical mechanics with projection-operator techniques. We extend the projection operators in order to include the effects of coarse-graining and the displacement field. As a result we obtain the time-evolution equations for the relevant variables with three kinds of terms on the right-hand sides: reversible, dissipative, and fluctuating terms. We find explicit formulas for the transport coefficients which are exact in the limit of continuum mechanics if the projection operators are properly defined. By construction the theory allows the diffusion of particles in terms of point defects where, however, in a normal crystal this diffusion is suppressed.

cond-mat.stat-mech↗

arXiv2022

The way from microscopic many-particle theory to macroscopic hydrodynamics

Starting from the microscopic description of a normal fluid in terms of any kind of local interacting many-particle theory we present a well defined step by step procedure to derive the hydrodynamic equations for the macroscopic phenomena. We specify the densities of the conserved quantities as the relevant hydrodynamic variables and apply the methods of non-equilibrium statistical mechanics with projection operator techniques. As a result we obtain time-evolution equations for the hydrodynamic variables with three kinds of terms on the right-hand sides: reversible, dissipative and fluctuating terms. In their original form these equations are completely exact and contain nonlocal terms in space and time which describe nonlocal memory effects. Applying a few approximations the nonlocal properties and the memory effects are removed. As a result we find the well known hydrodynamic equations of a normal fluid with Gaussian fluctuating forces. In the following we investigate if and how the time-inversion invariance is broken and how the second law of thermodynamics comes about. Furthermore, we show that the hydrodynamic equations with fluctuating forces are equivalent to stochastic Langevin equations and the related Fokker-Planck equation. Finally, we investigate the fluctuation theorem and find a modification by an additional term.

cond-mat.stat-mech↗

arXiv2021

Elasticity in crystals with high density of local defects : insights from ultra-soft colloids

In complex crystals close to melting or at finite temperatures, different types of defects are ubiquitous and their role becomes relevant in the mechanical response of these solids. Conventional elasticity theory fails to provide a microscopic basis to include and account for the motion of point-defects in an otherwise ordered crystalline structure. We study the elastic properties of a point-defect rich crystal within a first-principles theoretical framework derived from microscopic equations of motion. This framework allows us to make specific predictions pertaining to the mechanical properties which we can validate through deformation experiments performed in Molecular Dynamics simulations.

cond-mat.soft↗

arXiv2012

Quantum mechanical limitations to spin diffusion in the unitary Fermi gas

We compute spin transport in the unitary Fermi gas using the strong-coupling Luttinger-Ward theory. In the quantum degenerate regime the spin diffusivity attains a minimum value of $D_s \simeq 1.3 \hbar/m$ approaching the quantum limit of diffusion for a particle of mass $m$. Conversely, the spin drag rate reaches a maximum value of $Γ_\sd \simeq 1.2 k_B T_F/\hbar$ in terms of the Fermi temperature $T_F$. The frequency-dependent spin conductivity $σ_s(ω)$ exhibits a broad Drude peak, with spectral weight transferred to a universal high-frequency tail $σ_s(ω\to\infty) = \hbar^{1/2}C/3π(mω)^{3/2}$ proportional to the Tan contact density $C$. For the spin susceptibility $χ_s(T)$ we find no downturn in the normal phase.

cond-mat.quant-gas↗

arXiv2012

Renormalization-group calculation of the superfluid/normal-fluid interface of liquid 4He in gravity near T_lambda

The superfluid/normal-fluid interface of liquid 4He is investigated in gravity on earth where a small heat current Q flows vertically upward or downward. We present a local space- and time-dependent renormalization-group (RG) calculation based on model F which describes the dynamic critical effects for temperatures T near the superfluid transition T_lambda. The model-F equations are rewritten in a dimensionless renormalized form and solved numerically as partial differential equations. Perturbative corrections are included for the spatially inhomogeneous system within a self-consistent one-loop approximation. The RG flow parameter is determined locally as a function of space and time by a constraint equation which is solved by a Newton iteration. As a result we obtain the temperature profile of the interface. Furthermore we calculate the average order parameter , the correlation length xi, the specific heat C_Q and the thermal resistivity rho_T where we observe a rounding of the critical singularity by the gravity and the heat current. We compare the thermal resistivity with an experiment and find good qualitative agreement. Moreover we discuss our previous approach for larger heat currents and the self-organized critical state and show that our theory agrees with recent experiments in this latter regime.

cond-mat.stat-mech↗

arXiv2010

Viscosity and scale invariance in the unitary Fermi gas

We compute the shear viscosity of the unitary Fermi gas above the superfluid transition temperature, using a diagrammatic technique that starts from the exact Kubo formula. The formalism obeys a Ward identity associated with scale invariance which guarantees that the bulk viscosity vanishes identically. For the shear viscosity, vertex corrections and the associated Aslamazov-Larkin contributions are shown to be crucial to reproduce the full Boltzmann equation result in the high-temperature, low fugacity limit. The frequency dependent shear viscosity $η(ω)$ exhibits a Drude-like transport peak and a power-law tail at large frequencies which is proportional to the Tan contact. The weight in the transport peak is given by the equilibrium pressure, in agreement with a sum rule due to Taylor and Randeria. Near the superfluid transition the peak width is of the order of $0.5 T_F$, thus invalidating a quasiparticle description. The ratio $η/s$ between the static shear viscosity and the entropy density exhibits a minimum near the superfluid transition temperature whose value is larger than the string theory bound $\hbar/(4πk_B)$ by a factor of about seven.

cond-mat.quant-gas↗

arXiv1999

Renormalization-group theory for rotating 4He near the superfluid transition

The influence of a uniform rotation with frequency Omega on the critical behavior of liquid 4He near T_lambda is investigated. We apply our recently developed approach which is a renormalization-group theory based on model F starting with the calculation of the Green's function in Hartree approximation. We calculate the specific heat, the correlation length, and the thermal resistivity tensor as functions of the temperature T for fixed values of the rotation frequency Omega. For nonzero Omega we find that all physical quantities are smooth near T_lambda so that the superfluid transition is a smooth crossover. We define a frequency-dependent transition temperature T_lambda(Omega) by the maximum of the specific heat and present a power law prediction. For T<T_lambda(Omega) we find mutual friction between the superfluid and the normal-fluid component caused implicitly by the motion of vortex lines and calculate the Vinen coefficients B and B'.

cond-mat↗

arXiv1999

Liquid 4He near the superfluid transition in the presence of a heat current and gravity

The effects of a heat current and gravity in liquid 4He near the superfluid transition are investigated for temperatures above and below T_lambda. We present a renormalization-group calculation based on model F for the Green's function in a self-consistent approximation which in quantum many-particle theory is known as the Hartree approximation. The approach can handle a zero average order parameter above and below T_lambda and includes effects of vortices. We calculate the thermal conductivity and the specific heat for all temperatures T and heat currents Q in the critical regime. Furthermore, we calculate the temperature profile. Below T_lambda we find a second correlation length which describes the dephasing of the order parameter field due to vortices. We find dissipation and mutual friction of the superfluid-normal fluid counterflow and calculate the Gorter-Mellink coefficient A. We compare our theoretical results with recent experiments.

cond-mat↗

arXiv1999

Heat transport and self-organized criticality in liquid 4He close to T_lambda

We present a renormalization-group calculation based on model F for the thermal conductivity lambda_T(T,Q) in the presence of a homogeneous heat current Q and gravity. For temperatures below T_lambda we obtain a large but finite thermal conductivity corresponding to superfluid 4He with dissipation. Furthermore, we consider the self-organized critical state where the effects of gravity and heat current cancel each other so that the distance from criticality delta T = T(z) - T_lambda(z) is constant in space and a function of Q. We compare our theoretical results with recent experiments.

cond-mat↗