arXiv subjects

T. R. Kirkpatrick

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

At least 55 records · Page 3Linked to original sources

arXiv2017

Quantum triple point and quantum critical endpoints in metallic magnets

In low-temperature metallic magnets, ferromagnetic (FM) and antiferromagnetic (AFM) orders can exist in a single system in different parts of the phase diagram as a function of some control parameter. These phases can be adjacent, or exist concurrently, resulting in a phase transition between a FM phase and an AFM one, or between a phase of concurrent FM and AFM order and either of the pure phases. We show that universal quantum fluctuations qualitatively alter the known phase diagrams for classical magnets: They shrink the region of concurrent FM and AFM order, change various transitions from second to first order, and, in the presence of a magnetic field, lead to either a quantum triple point where the FM, AFM and paramagnetic phases coexist, or to a quantum critical end point.

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arXiv2017

Spin dynamics of antiferromagnets in the presence of a homogeneous magnetization

We use general hydrodynamic equations to determine the long-wavelength spin excitations in isotropic antiferromagnets in the presence of a homogeneous magnetization. The latter may be induced, such as in antiferromagnets in an external magnetic field, or spontaneous, such as in ferrimagnetic or canted phases that are characterized by the coexistence of antiferromagnetic and ferromagnetic order. Depending on the physical situation, we find propagating spin waves that are gapped in some cases and gapless in others, diffusive modes, or relaxational modes. The excitation spectra turn out to be qualitatively different depending on whether or not the homogeneous magnetization is a conserved quantity. The results lay the foundation for a description of a variety of quantum phase transitions, including the transition from a ferromagnetic metal to an antiferromagnetic one, and the spin-flop transitions that are observed in some antiferromagnets. They also are crucial for incorporating weak-localization and Altshuler-Aronov effects into the descriptions of quantum phases in both clean and disordered magnetic metals.

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arXiv2017

Contrasting work fluctuations and distributions in systems with short-range and long-range correlations

It is shown that the work fluctuations and work distribution functions are fundamentally different in systems with short-range versus long-range correlations. The two cases considered with long- range correlations are magnetic work fluctuations in an equilibrium isotropic ferromagnet, and work fluctuations in a non-equilibrium fluid with a temperature gradient. The long-range correlations in the former case are due to equilibrium Goldstone modes, while in the latter they are due to generic non-equilibrium effects. The magnetic case is of particular interest since an external magnetic field can be used to tune the system from one with long-range correlations, to one with only short- range correlations. It is shown that in systems with long-range correlations the work distribution is extraordinarily broad compared to systems with only short-range correlations. Surprisingly these results imply that fluctuations theorems such as the Jarzynski fluctuation theorem are more useful in systems with long-range correlations than in systems with short-range correlations.

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arXiv2016

Work, work fluctuations, and the work distribution in a thermal non-equilibrium steady state

Long-ranged correlations generically exist in non-equilibrium fluid systems. In the case of a non-equilibrium steady state caused by a temperature gradient the correlations are especially long-ranged and strong. The anomalous light scattering predicted to exist in these systems is well-confirmed by numerous experiments. Recently the Casimir force or pressure due to these fluctuations or correlations have been discussed in great detail. In this paper the notion of a Casimir work is introduced and a novel way to measure the non-equilibrium Casimir force is suggested. In particular, the non-equilibrium Casimir force is related to a non-equilibrium heat and not, as in equilibrium, to a volume derivative of an average energy. The non-equilibrium work fluctuations are determined and shown to be very anomalous compared to equilibrium work fluctuations. The non-equilibrium work distribution is also computed, and contrasted to work distributions in systems with short-range correlations. Again, there is a striking difference in the two cases. Formal theories of work and work distributions in non-equilibrium steady states are not explicit enough to illustrate any of these interesting features.

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arXiv2016

Scaling Theory of a Compressibility-Driven Metal-Insulator Transition in a Two-Dimensional Electron Fluid

We present a scaling description of a metal-insulator transition in two-dimensional electron systems that is driven by a vanishing compressibility rather than a vanishing diffusion coefficient. A small set of basic assumptions leads to a consistent theoretical framework that is compatible with existing transport and compressibility measurements, and allows to make predictions for other observables. We also discuss connections between these ideas and other theories of transitions to an incompressible quantum fluid.

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arXiv2016

Magnon-induced long-range correlations and their neutron-scattering signature in quantum magnets

We consider the coupling of the magnons in both quantum ferromagnets and antiferromagnets to the longitudinal order-parameter fluctuations, and the resulting nonanalytic behavior of the longitudinal susceptibility. In classical magnets it is well known that long-range correlations induced by the magnons lead to a singular wave-number dependence of the form $1/k^{4-d}$ in all dimensions 2<d<4, for both ferromagnets and antiferromagnets. At zero temperature we find a profound difference between the two cases. Consistent with naive power counting, the longitudinal susceptibility in a quantum antiferromagnet scales as $k^{d-3}$ for 1<d<3, whereas in a quantum ferromagnet the analogous result, $k^{d-2}$, is absent due to a zero scaling function. This absence of a nonanalyticity in the longitudinal susceptibility is due to the lack of magnon number fluctuations in the ground state of a quantum ferromagnet; correlation functions that are sensitive to other fluctuations do exhibit the behavior predicted by simple power counting. Also of interest is the dynamical behavior as expressed in the longitudinal part of the dynamical structure factor, which is directly measurable via neutron scattering. For both ferromagnets and antiferromagnets there is a logarithmic singularity at the magnon frequency with a prefactor that vanishes as $T\to 0$. In the antiferromagnetic case there also is a nonzero contribution at T=0 that is missing for ferromagnets. Magnon damping due to quenched disorder restores the expected scaling behavior of the longitudinal susceptibility in the ferromagnetic case; it scales as $k^{d-2}$ if the order parameter is not conserved, or as $k^d$ if it is. Detailed predictions are made for both two- and three-dimensional systems at both T=0 and in the limit of low temperatures, and the physics behind the various nonanalytic behaviors is discussed.

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arXiv2016

The quantum ferromagnetic transition in a clean Kondo lattice is discontinuous

The Kondo-lattice model, which couples a lattice of localized magnetic moments to conduction electrons, is often used to describe heavy-fermion systems. Because of the interplay between Kondo physics and magnetic order it displays very complex behavior and is notoriously hard to solve. The ferromagnetic Kondo-lattice model, with a ferromagnetic coupling between the local moments, describes a phase transition from a paramagnetic phase to a ferromagnetic one as a function of either temperature or the ferromagnetic local-moment coupling. At zero temperature, this is a quantum phase transition that has received considerable attention. It has been theoretically described to be continuous, or second order. Here we show that this belief is mistaken; in the absence of quenched disorder the quantum phase transition is first order, in agreement with experiments, as is the corresponding transition in other metallic ferromagnets.

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arXiv2016

Droplet formation near first-order phase transitions: A mechanism for heterogeneity and phase separation away from the coexistence curve

Phase separation, i.e., the coexistence of two different phases, is observed in many systems away from the coexistence curve of a first-order transition, leading to a stable heterogeneous phase or region. Examples include various quantum ferromagnets, heavy-fermion systems, rare-earth nickelates, and others. These observations seem to violate basic notions of equilibrium thermodynamics, which state that phase separation can occur only on the coexistence curve. We show theoretically that quenched disorder allows for phase separation away from the coexistence curve even in equilibrium due to the existence of stable minority-phase droplets within the majority phase. Our scenario also answers a related question: How can a first-order transition remain sharp in the presence of quenched disorder without violating the rigorous lower bound $ν\geq 2/d$ for the correlation-length exponent? We discuss this scenario in the context of experimental results for a large variety of systems.

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arXiv2016

Nonequilibrium fluctuation-induced Casimir pressures in liquid mixtures

In this article we derive expressions for Casimir-like pressures induced by nonequilibrium concentration fluctuations in liquid mixtures. The results are then applied to liquid mixtures in which the concentration gradient results from a temperature gradient through the Soret effect. A comparison is made between the pressures induced by nonequilibrium concentration fluctuations in liquid mixtures and those induced by nonequilibrium temperature fluctuations in one-component fluids. Some suggestions for experimental verification procedures are also presented.

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arXiv2016

Physical origin of nonequilibrium fluctuation-induced forces in fluids

Long-range thermal fluctuations appear in fluids in nonequilibrium states leading to fluctuation-induced Casimir-like forces. Two distinct mechanisms have been identified for the origin of the long-range nonequilibrium fluctuations in fluids subjected to a temperature or concentration gradient. One is a coupling between the heat or mass-diffusion mode with a viscous mode in fluids subjected to a temperature or concentration gradient. Another one is the spatial inhomogeneity of thermal noise in the presence of a gradient. We show that in fluids fluctuation-induced forces arising from mode coupling are several orders of magnitude larger than those from inhomogeneous noise.

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arXiv2015

Why Non-equilibrium is Different

The 1970 paper, "Decay of the Velocity Correlation Function" [Phys. Rev. A1, 18 (1970), see also Phys. Rev. Lett. 18, 988 (1967)] by Berni Alder and Tom Wainwright, demonstrated, by means of computer simulations, that the velocity autocorrelation function for a particle in a gas of hard disks decays algebraically in time as $t^{-1},$ and as $t^{-3/2}$ for a gas of hard spheres. These decays appear in non-equilibrium fluids and have no counterpart in fluids in thermodynamic equilibrium. The work of Alder and Wainwright stimulated theorists to find explanations for these "long time tails" using kinetic theory or a mesoscopic mode-coupling theory. This paper has had a profound influence on our understanding of the non-equilibrium properties of fluid systems. Here we discuss the kinetic origins of the long time tails, the microscopic foundations of mode-coupling theory, and the implications of these results for the physics of fluids. We also mention applications of the long time tails and mode-coupling theory to other, seemingly unrelated, fields of physics. We are honored to dedicate this short review to Berni Alder on the occasion of his 90th birthday!

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arXiv2015

Non-equilibrium concentration fluctuations in binary liquids with realistic boundary conditions

Because of the spatially long-ranged nature of spontaneous fluctuations in thermal non-equilibrium systems, they are affected by boundary conditions for the fluctuating hydrodynamic variables. In this paper we consider a liquid mixture between two rigid and impervious plates with a stationary concentration gradient resulting from a temperature gradient through the Soret effect. For liquid mixtures with a large Lewis number, we are able to obtain explicit analytical expressions for the intensity of the non-equilibrium concentration fluctuations as a function of the frequency $ω$ and the wave number $q$ of the fluctuations. In addition we elucidate the spatial dependence of the intensity of the non-equilibrium fluctuations responsible for a non-equilibrium Casimir effect.

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arXiv2015

Exponent relations at quantum phase transitions, with applications to metallic quantum ferromagnets

Relations between critical exponents, or scaling laws, at both continuous and discontinuous quantum phase transitions are derived and discussed. In general there are multiple dynamical exponents at these transitions, which complicates the scaling description. Some rigorous inequalities are derived, and the conditions needed for these inequalities to be equalities are discussed. New scaling laws involving the specific-heat exponents are derived and and contrasted with their counterparts at classical phase transitions. We also generalize the ideas of Fisher and Berker and others for applying (finite-size) scaling theory near a classical first-order transition to the quantum case. We then apply and illustrate all of these ideas by using the quantum ferromagnetic phase transition in metals as an explicit example. This transition is known to have multiple dynamical scaling exponents, and in general it is discontinuous in clean systems, but continuous in disordered ones. Furthermore, it displays many experimentally relevant crossover phenomena that can be described in terms of fixed points, originally discussed by Hertz, that ultimately become unstable asymptotically close to the transition and give way to the asymptotic fixed points. These fixed points provide a rich environment for illustrating the general scaling concepts and exponent relations. We also discuss the quantum-wing critical point at the tips of the tricritical wings associated with the discontinuous quantum ferromagnetic transition from a scaling point of view.

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arXiv2015

Metallic Quantum Ferromagnets

This review gives an overview of the quantum phase transition (QPT) problem in metallic ferromagnets, discussing both experimental and theoretical aspects. These QPTs can be classified with respect to the presence and strength of quenched disorder: Clean systems generically show a discontinuous, or first-order, QPT from the ferromagnetic state to a paramagnetic one as a function of some control parameter, as predicted by theory. Disordered systems are much more complicated, depending on the disorder strength and the distance from the QPT. In many disordered materials the QPT is continuous, or second order, and Griffiths-phase effects coexist with QPT singularities near the transition. In other systems the transition from the ferromagnetic state at low temperatures is to a different type of long-range order, such as an antiferromagnetic or a spin-density-wave state. In still other materials a transition to a state with glass-like spin dynamics is suspected. The review provides a comprehensive discussion of the current understanding of these various transitions, and of the relation between experimental and theoretical developments.

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arXiv2015

Quantum Correlations in Metals that Grow in Time and Space

We show that the correlations of electrons with a fixed energy in metals have very anomalous time and space dependences. Due to soft modes that exist in any Fermi liquid, combined with the incomplete screening of the Coulomb interaction at finite frequencies, the correlations in 2-d systems grow with time as $t^2$. In the presence of disorder, the spatial correlations grow as the distance squared. Similar, but in general weaker, effects are present in 3-d systems and in the absence of quenched disorder. We propose ways to experimentally measure these anomalous correlations.

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arXiv2015

Non-Equilibrium is Different

Non-equilibrium and equilibrium fluid systems differ due to the existence of long-range correlations in non-equilibrium that are not present in equilibrium, except at critical points. Here we examine fluctuations of the temperature, of the pressure tensor, and of the heat current in a fluid maintained in a non-equilibrium stationary state (NESS) with a fixed temperature gradient, a system where the non-equilibrium correlations are especially long ranged. For this particular NESS our results show that (1) The mean-squared fluctuations in non-equilibrium differ markedly in their system size scaling compared to their equilibrium counterparts and (2) There are large, nonlocal, correlations of the normal stress in this NESS. These terms provide important corrections to the fluctuating normal stress in linearized Landau-Lifshitz fluctuating hydrodynamics.

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arXiv2015

Third law of thermodynamics and the shape of the phase diagram for systems with a first-order quantum phase transition

The Third Law of Thermodynamics constrains the phase diagram of{systems with a first-order quantum phase transition. For zero conjugate field, the coexistence curve has an infinite slope at T=0. If a tricritical point exists at T>0, then the associated tricritical wings are perpendicular to the T=0 plane, but not to the zero-field plane. These results are based on the third law and basic thermodynamics only, and are completely general. As an explicit example we consider the ferromagnetic quantum phase transition in clean metals, where a first-order quantum phase transition is commonly observed.

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arXiv2015

Non-equilibrium Casimir-like Forces in Liquid Mixtures

In this Letter we consider a liquid mixture confined between two thermally conducting walls subjected to a stationary temperature gradient. While in a one-component liquid non-equilibrium fluctuation forces appear inside the liquid layer only, non-equilibrium fluctuations in a mixture induce a Casimir-like force on the walls. The physical reason is that the temperature gradient induces large concentration fluctuations through the Soret effect. Unlike temperature fluctuations, non-equilibrium concentration fluctuations are also present near a perfectly thermally conducting wall. The magnitude of the fluctuation-induced Casimir force is proportional to the square of the Soret coefficient and is related to the concentration dependence of the heat and volume of mixing.

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