arXiv subjects

T. R. Kirkpatrick

Publications and source records attributed to T. R. Kirkpatrick.

At least 37 records · Page 2Linked to original sources

arXiv2020

RFOT theory for glassy dynamics in a single condensed polymer

The number of compact structures of a single condensed polymer (SCP), with similar free energies, grows exponentially with the degree of polymerization. In analogy with structural glasses (SGs), we expect that at low temperatures chain relaxation should occur by activated transitions between the compact metastable states. By evolving the states of the SCP that is linearly coupled to a reference state, we show that, below a dynamical transition temperature ($T_d$), the SCP is trapped in a metastable state leading to slow dynamics. At a lower temperature, $T_K \ne 0$, the configurational entropy vanishes, resulting in a thermodynamic random first order ideal glass transition. The relaxation time obeys the Vogel-Fulcher-Tamman law, diverging at $T=T_0 \approx T_K$. These findings, accord well with the random first order transition theory, establishing that SCP and SG exhibit similar universal characteristics.

cond-mat.soft↗

arXiv2020

Exact solution of the Boltzmann equation for low-temperature transport coefficients in metals I: Scattering by phonons, antiferromagnons, and helimagnons

We present a technique for an exact solution of the linearized Boltzmann equation for the electrical and thermal transport coefficients in metals in the low-temperature limit. This renders unnecessary an uncontrolled approximation that has been used in all previous solutions of the integral equations for the transport coefficients. Applications include electron-phonon scattering in nonmagnetic metals, as well as the magnon contribution to the electrical and thermal conductivities, and to the thermopower, in metallic ferromagnets, antiferromagnets, and helimagnets. In this paper, the first of a pair, we set up the technique and apply it to the scattering of electrons by phonons, antiferromagnons, and helimagnons. We show that the Bloch $T^5$ law for the electrical resistivity, the $T^2$ law for the thermal resistivity, and the $T$ law for the thermopower due to phonon and antiferromagnon scattering are exact, and determine the prefactors exactly. The corresponding exact results for helimagnons are $T^{5/2}$, $T^{1/2}$, and $T$, respectively. In a second paper we will consider the scattering by ferromagnons.

cond-mat.stat-mech↗

arXiv2020

Exact solution of the Boltzmann equation for low-temperature transport coefficients in metals II: Scattering by ferromagnons

In a previous paper (Paper I) we developed a technique for exactly solving the linearized Boltzmann equation for the electrical and thermal transport coefficients in metals in the low-temperature limit. Here we adapt this technique to determine the magnon contribution to the electrical and thermal conductivities, and to the thermopower, in metallic ferromagnets. For the electrical resistivity $ρ$ at asymptotically low temperatures we find $ρ\propto \exp{(-T_{\rm min}/T)}$, with $T_{\rm min}$ an energy scale that results from the exchange gap and a temperature independent prefactor of the exponential. The corresponding result for the heat conductivity is $σ_h \propto T^3\,\exp{(T_{\rm min}/T)}$, and thermopower is $S \propto T$. All of these results are exact, including the prefactors.

cond-mat.stat-mech↗

arXiv2020

Ferromagnetic Quantum Critical Point in Non-Centrosymmetric Systems

Ferromagnetic quantum criticality in clean metals has proven elusive due to fermionic soft modes that drive the transition first order. We show that non-centrosymmetric metals with a strong spin-orbit interaction provide a promising class of materials for realizing a ferromagnetic quantum critical point in clean systems. The spin-orbit interaction renders massive the soft modes that interfere with quantum criticality in most materials, while the absence of spatial inversion symmetry precludes the existence of new classes of soft modes that could have the same effect.

cond-mat.str-el↗

arXiv2020

Rigorous results for the electrical conductivity due to electron-phonon scattering

We present a rigorous solution of the Boltzmann equation for the electron-phonon scattering problem in three spatial dimensions in the limit of low temperatures. The different temperature scaling of the various scattering rates turns the temperature into a control parameter that is not available in classical kinetic theory and allows for a rigorous proof of Bloch's $T^5$ law. The relation between the Boltzmann equation and the Kubo formula is also discussed, as well as implications for the scattering of electrons by excitations other than phonons.

math-ph↗

arXiv2019

Transition to Turbulence in Driven Active Matter

A Lorenz-like model was set up recently, to study the hydrodynamic instabilities in a driven active matter system. This Lorenz model differs from the standard one in that all three equations contain non-linear terms. The additional non-linear term comes from the active matter contribution to the stress tensor. In this work, we investigate the non-linear properties of this Lorenz model both analytically and numerically. The significant feature of the model is the passage to chaos through a complete set of period-doubling bifurcations above the Hopf point for inverse Schmidt numbers above a critical value. Interestingly enough, at these Schmidt numbers a strange attractor and stable fixed points coexist beyond the homoclinic point. At the Hopf point, the strange attractor disappears leaving a high-period periodic orbit. This periodic state becomes the expected limit cycle through a set of bifurcations and then undergoes a sequence of period-doubling bifurcations leading to the formation of a strange attractor. This is the first situation where a Lorenz-like model has shown a set of consecutive period-doubling bifurcations in a physically relevant transition to turbulence.

physics.flu-dyn↗

arXiv2019

Magnetic Quantum Phase Transitions in a Clean Dirac Metal

We consider clean Dirac metals where the linear band crossing is caused by a strong spin-orbit interaction, and study the quantum phase transitions from the paramagnetic phase to various magnetic phases, including homogeneous ferromagnets, ferrimagnets, canted ferromagnets, and magnetic nematics. We show that in all of these cases the coupling of fermionic soft modes to the order parameter generically renders the quantum phase transition first order, with certain gapless Dirac systems providing a possible exception. These results are surprising since a strong spin-orbit scattering suppresses the mechanism that causes the first order transition in ordinary metals. The important role of chirality in generating a new mechanism for a first-order transition is stressed.

cond-mat.str-el↗

arXiv2019

Fragile-to-Strong Crossover, growing length scales, and dynamic heterogeneity in Wigner Glasses

Colloidal particles, which are ubiquitous, have become ideal testing grounds for the structural glass transition (SGT) theories. In these systems glassy behavior is manifested as the density of the particles is increased. Thus, soft colloidal particles with varying degree of softness capture diverse glass forming properties, observed normally in molecular glasses. By performing Brownian dynamics simulations for a binary mixture of micron-sized charged colloidal suspensions, known to form Wigner glasses, we show that by tuning the softness of the potential, achievable by changing the monovalent salt concentration, there is a continuous transition between fragile to strong behavior. Remarkably, this is found in a system where the well characterized potential between the colloidal particles is isotropic. We also show that the predictions of the random first order transition (RFOT) theory quantitatively describes the universal features such as the growing correlation length, $ξ\sim (ϕ_K/ϕ- 1)^{-ν}$ with $ν= 2/3$ where $ϕ_K$, the analogue of the Kauzmann temperature, depends on the salt concentration. As anticipated by the RFOT predictions, we establish a causal relationship between the growing correlation length and a steep increase in the relaxation time and dynamic heterogeneity. The broad range of fragility observed in Wigner glasses is used to draw analogies with molecular glasses. The large variations in the fragility is found only when the temperature dependence of the viscosity is examined for a large class of diverse glass forming materials. In sharp contrast, this is vividly illustrated in a single system that can be experimentally probed. Our work also shows that the RFOT predictions are accurate in describing the dynamics over the entire density range, regardless of the fragility of the glasses, implying that the physics describing the SGT is universal.

cond-mat.soft↗

arXiv2019

Nonequilibrium Casimir pressures in liquids under shear

In stationary nonequilibrium states coupling between hydrodynamic modes causes thermal fluctuations to become long ranged inducing nonequilibrium Casimir pressures. Here we consider nonequilibrium Casimir pressures induced in liquids by a velocity gradient. Specifically, we have obtained explicit expressions for the magnitude of the shear-induced pressure enhancements in a liquid layer between two horizontal plates that complete and correct results previously presented in the literature. In contrast to nonequilibrium Casimir pressures induced by a temperature or concentration gradient, we find that in shear nonequilibrium contributions from short-range fluctuations are no longer negligible. In addition, it is noted that currently available computer simulations of model fluids in shear observe effects from molecular correlations at nanoscales that have a different physical origin and do not probe shear-induced pressures resulting from coupling of long-wavelength hydrodynamic modes. Even more importantly, we find that in actual experimental conditions, shear-induced pressure enhancements are caused by viscous heating and not by thermal velocity fluctuations. Hence, isothermal computer simulations are irrelevant for the interpretation of experimental shear-induced pressure enhancements.

cond-mat.stat-mech↗

arXiv2019

Quantum Ferromagnetic Transition in Clean Dirac Metals

The ferromagnetic quantum phase transition in clean metals with a negligible spin-orbit interaction is known to be first order due to a coupling of the magnetization to soft fermionic particle-hole excitations. A spin-orbit interaction gives these excitations a mass, suggesting the existence of a ferromagnetic quantum critical point in metals with a strong spin-orbit interaction. We show that this expectation is not borne out in a large class of materials with a Dirac spectrum, since the chirality degree of freedom leads to new soft modes that again render the transition first order.

cond-mat.str-el↗

arXiv2019

Driven active matter: fluctuations and a hydrodynamic instability

Wet active matter in the presence of an imposed temperature gradient, or chemical potential gradient, is considered. It is shown that there is a new type of convective instability that is caused by a (negative) activity parameter. Physically this corresponds to active fluids with contractual stress. In this non-equilibrium steady state the singular generic long-ranged correlations are computed and compared with the analogous results in a passive fluid. In addition, the singular non-equlibirum Casimir pressure or force is determined. The fluid motion above the instability is determined by generalizing the Lorenz equations for the Rayleigh-Benard instability in a passive fluid to Lorenz-like equations to describe this new instability.

cond-mat.soft↗

arXiv2019

Soft Modes and Nonanalyticities in a Clean Dirac Metal

We consider the effects of the electron-electron interaction in a clean Dirac metal, i.e., a Dirac system with the chemical potential not tuned to the Dirac point. We introduce the notion of a Dirac Fermi liquid (DFL) and discuss the soft two-particle excitations in such systems, which are qualitatively different from the corresponding excitations in a conventional, or Landau, Fermi liquid (LFL). These soft excitations lead to nonanalytic dependencies of observables, including the density of states, the spin susceptibility, and the specific heat, on the temperature, magnetic field, and wave number, which first appear at second order in the interaction. We determine and discuss the nature of these nonanalyticities in a DFL and compare them with the corresponding effects in a LFL. Our results are based on very general arguments regarding the existence and nature of the soft modes, and corroborated by explicit perturbative calculations. We also discuss their consequences for magnetic quantum phase transitions in Dirac metals.

cond-mat.str-el↗

arXiv2019

Shear-induced Casimir forces in liquid layers

In stationary nonequilibrium states a coupling between hydrodynamic modes causes thermal fluctuations to become long ranged inducing nonequilibrium Casimir forces or pressures. Here we consider nonequilibrium Casimir pressures induced in liquids by a velocity gradient. Specifically, we have obtained explicit expressions for the magnitude of the shear-induced pressure enhancement in a liquid layer between two horizontal plates that complete and correct results previously presented in the literature. In contrast to nonequiibrium Casimir pressures induced by a temperature gradient, kinetic theory shows that nonequilibrium contributions from short-range fluctuations are no longer negligible. In addition, it is noted that computer simulations of model fluids in shear observe effects from molecular correlations at nanoscales that have a different physical origin. The idea that such computer simulations probe shear-induced pressures resulting from coupling of long-wavelength hydrodynamic modes is erroneous.

cond-mat.stat-mech↗

arXiv2018

Anomalous Transport Behavior in Quantum Magnets

Transport behavior characterized by a low-temperature electrical resistivity that displays a power-law behavior $ρ(T\to 0) \propto T^s$ with an exponent $s<2$, is commonly observed in magnetic materials in both the magnetic and nonmagnetic phases. We give a pedagogical overview of this phenomenon that summarizes both the experimental situation and the state of its theoretical understanding. We also put it in context by drawing parallels with unusual power-law transport behavior in other systems.

cond-mat.str-el↗

arXiv2018

Fluctuations, renormalizations, and a convective instability in driven wet active matter

A scalar model of wet active matter in the presence of an imposed temperature gradient, or chemical potential gradient, is considered. It is shown that there is a convective instability driven by a (negative) activity parameter. In this non-equilibrium steady state the generic long-ranged correlations are computed and compared and contrasted with the analogous results in a passive fluid. In addition, the non-equilibrium Casimir pressure or force is computed. Singularities in various physical quantities as the instability is approached are determined. Finally, we give the generalized Lorenz equations characterizing the fluid behavior above the instability and contrast these equations to the Lorenz equations for the Rayleigh-Bernard instability in a passive fluid.

cond-mat.soft↗

arXiv2018

Generic non-Fermi-liquid behavior of the resistivity in magnets with ferromagnetic, helical, or skyrmionic order

The electrical resistivity of several relatively clean metallic ferromagnets, as well as the helimagnet MnSi, is commonly observed to exhibit non-Fermi-liquid behavior at low temperatures. This behavior, which is found in both ordered and disordered phases, and both near and away from the magnetic transition, remains a major unsolved problem. We derive and discuss three novel mechanisms underlying such behavior that are based on electron scattering mediated by the exchange of (1) ferromagnons or (2) skyrmionic fluctuations, both in conjunction with weak disorder, or (3) helimagnons in clean systems. Since the magnetic transition in weakly disordered sytems is generically discontinuous, static droplets of the ordered phase can exist within the disordered phase, making the mechanisms viable there as well. We compare our theoretical results with existing experimental ones and suggest additional experiments.

cond-mat.str-el↗

arXiv2017

Work probability distribution for a ferromagnet with long-ranged and short-ranged correlations

Work fluctuations and work probability distributions are fundamentally different in systems with short- ranged versus long-ranged correlations. Specifically, in systems with long-ranged correlations the work distribution is extraordinarily broad compared to systems with shortranged correlations. This difference profoundly affects the possible applicability of fluctuation theorems like the Jarzynski fluctuation theorem. The Heisenberg ferromagnet , well below its Curie temperature, is a system with long-ranged correlations in very low magnetic fields due to the presence of Goldstone modes. As the magnetic field is increased the correlations gradually become short-ranged. Hence, such a ferromagnet is an ideal system for elucidating the changes of the work probability distribution as one goes from a domain with long-ranged correlations to a domain with short-ranged correlations by tuning the magnetic field. A quantitative analysis of this crossover behaviour of the work probability distribution and the associated fluctuations is presented.

cond-mat.stat-mech↗

arXiv2017

Giant Casimir non-equilibrium forces drive coil to globule transition in polymers

We develop a theory to probe the effect of non-equilibrium fluctuation-induced forces on the size of a polymer confined between two horizontal thermally conductive plates subject to a constant temperature gradient, $\nabla T$. We assume that (a) the solvent is good and (b) the distance between the plates is large so that in the absence of a thermal gradient the polymer is a coil whose size scales with the number of monomers as $N^ν$, with $ν\approx 0.6$. We predict that above a critical temperature gradient, $\nabla T_c \sim N^{-\frac{5}{4}}$, favorable attractive monomer-monomer interaction due to Giant Casimir Force (GCF) overcomes the chain conformational entropy, resulting in a coil-globule transition. The long-ranged GCF-induced interactions between monomers, arising from thermal fluctuations in non-equilibrium steady state, depend on the thermodynamic properties of the fluid. Our predictions can be verified using light-scattering experiments with polymers, such as polystyrene or polyisoprene in organic solvents (neopentane) in which GCF is attractive.

cond-mat.stat-mech↗