Zero-temperature Limit Research Articles

Velocity distribution functions and intermittency in one-dimensional randomly forced Burgers turbulence

The problem of one-dimensional randomly forced Burgers turbulence is considered in terms of directed polymers. In the limit of strong turbulence (which corresponds to the zero temperature limit for a directed polymer system), a general explicit expression for the joint distribution function of two velocities separated by a finite distance is derived using the replica technique. In particular, it is shown that at length scales much smaller than the injection length of the Burgers random force, the moments of the velocity increment exhibit typical strong intermittency behavior.

Zero-temperature limit of thermodynamic quantum master equations

We investigate the zero-temperature limit of thermodynamic quantum master equations that govern the time evolution of density matrices for dissipative quantum systems. The quantum master equations for $T=0$ and for $T>0$ possess completely different structures: (i) the equation for $T=0$ is linear in the deviation from the ground-state density matrix, whereas the equation for $T>0$, in general, is seriously nonlinear, and (ii) the Gibbs state is obtained as the steady-state solution of the nonlinear equation for $T>0$, whereas the ground state cannot be found from the equation for $T=0$. Nevertheless, the equation for $T=0$ can reproduce the behavior for $T\ensuremath{\gtrsim}0$ remarkably well. We discuss some implications of that observation for dissipative quantum field theory.

Zero Temperature Limit for Directed Polymers and Inviscid Limit for Stationary Solutions of Stochastic Burgers Equation

We consider a space-continuous and time-discrete polymer model for positive temperature and the associated zero temperature model of last passage percolation type. In our previous work, we constructed and studied infinite-volume polymer measures and one-sided infinite minimizers for the associated variational principle, and used these objects for the study of global stationary solutions of the Burgers equation with positive or zero viscosity and random kick forcing, on the entire real line. In this paper, we prove that in the zero temperature limit, the infinite-volume polymer measures concentrate on the one-sided minimizers and that the associated global solutions of the viscous Burgers equation with random kick forcing converge to the global solutions of the inviscid equation.

From Monge\u2013Amp\xe8re equations to envelopes and geodesic rays in the zero temperature limit

Let (X,theta ) be a compact complex manifold X equipped with a smooth (but not necessarily positive) closed (1, 1)-form theta . By a well-known envelope construction this data determines, in the case when the cohomology class [theta ] is pseudoeffective, a canonical theta -psh function u_{theta }. When the class [theta ] is Kähler we introduce a family u_{beta } of regularizations of u_{theta }, parametrized by a large positive number beta , where u_{beta } is defined as the unique smooth solution of a complex Monge–Ampère equation of Aubin–Yau type. It is shown that, as beta rightarrow infty , the functions u_{beta } converge to the envelope u_{theta } uniformly on X in the Hölder space C^{1,alpha }(X) for any alpha in ]0,1[ (which is optimal in terms of Hölder exponents). A generalization of this result to the case of a nef and big cohomology class is also obtained and a weaker version of the result is obtained for big cohomology classes. The proofs of the convergence results do not assume any a priori regularity of u_{theta }. Applications to the regularization of omega -psh functions and geodesic rays in the closure of the space of Kähler metrics are given. As briefly explained there is a statistical mechanical motivation for this regularization procedure, where beta appears as the inverse temperature. This point of view also leads to an interpretation of u_{beta } as a “transcendental” Bergman metric.

Max $\kappa$-cut and the inhomogeneous Potts spin glass

We study the asymptotic behavior of the Max $\kappa$-cut on a family of sparse, inhomogeneous random graphs. In the large degree limit, the leading term is a variational problem, involving the ground state of a constrained inhomogeneous Potts spin glass. We derive a Parisi-type formula for the free energy of this model, with possible constraints on the proportions, and derive the limiting ground state energy by a suitable zero temperature limit.

Asymptotics of quantum weighted Hurwitz numbers

This work concerns both the semiclassical and zero temperature asymptotics of quantum weighted double Hurwitz numbers. The partition function for quantum weighted double Hurwitz numbers can be interpreted in terms of the energy distribution of a quantum Bose gas with vanishing fugacity. We compute the leading semiclassical term of the partition function for three versions of the quantum weighted Hurwitz numbers, as well as lower order semiclassical corrections. The classical limit is shown to reproduce the simple single and double Hurwitz numbers studied by Okounkov and Pandharipande (2000 Math. Res. Lett. 7 447–53, 2000 Lett. Math. Phys. 53 59–74). The KP-Toda τ-function that serves as generating function for the quantum Hurwitz numbers is shown to have the τ-function of Okounkov and Pandharipande (2000 Math. Res. Lett. 7 447–53, 2000 Lett. Math. Phys. 53 59–74) as its leading term in the classical limit, and, with suitable scaling, the same holds for the partition function, the weights and expectations of Hurwitz numbers. We also compute the zero temperature limit of the partition function and quantum weighted Hurwitz numbers. The KP or Toda τ-function serving as generating function for the quantum Hurwitz numbers are shown to give the one for Belyi curves in the zero temperature limit and, with suitable scaling, the same holds true for the partition function, the weights and the expectations of Hurwitz numbers.

Singular Temperature Dependence of the Equation of State of Superconductors with Spin-Orbit Interaction in Low-Temperature Region \u2013 II

We extend a previous study of the space and temperature dependence of the order parameter in an ultrathin superconducting film in a longitudinal magnetic field to the vicinity of the critical transition surface. In these films, the spin-orbit interaction can be sizeable. The calculations are restricted to the low-temperature regime. Special attention is given to the zero temperature limit where the state with the maximum value of the critical field is investigated for the given strength of the spin-orbit interaction.

Bizarre behavior of heat capacity in crystals due to interplay between two types of anharmonicities.

The heat capacity of classical crystals is determined by the Dulong-Petit value CV ≃ D (where D is the spatial dimension) for softly interacting particles and has the gas-like value CV ≃ D/2 in the hard-sphere limit, while deviations are governed by the effects of anharmonicity. Soft- and hard-sphere interactions, which are associated with the enthalpy and entropy of crystals, are specifically anharmonic owing to violation of a linear relation between particle displacements and corresponding restoring forces. Here, we show that the interplay between these two types of anharmonicities unexpectedly induces two possible types of heat capacity anomalies. We studied thermodynamics, pair correlations, and collective excitations in 2D and 3D crystals of particles with a limited range of soft repulsions to prove the effect of interplay between the enthalpy and entropy types of anharmonicities. The observed anomalies are triggered by the density of the crystal, changing the interaction regime in the zero-temperature limit, and can provide about 10% excess of the heat capacity above the Dulong-Petit value. Our results facilitate understanding effects of complex anharmonicity in molecular and complex crystals and demonstrate the possibility of new effects due to the interplay between different types of anharmonicities.

Color superconductivity from the chiral quark–meson model

We study the two-flavor color superconductivity of low-temperature quark matter in the vicinity of chiral phase transition in the quark–meson model where the interactions between quarks are generated by pion and sigma exchanges. Starting from the Nambu–Gorkov propagator in real-time formulation we obtain finite temperature (real axis) Eliashberg-type equations for the quark self-energies (gap functions) in terms of the in-medium spectral function of mesons. Exact numerical solutions of the coupled nonlinear integral equations for the real and imaginary parts of the gap function are obtained in the zero temperature limit using a model input spectral function. We find that these components of the gap display a complicated structure with the real part being strongly suppressed above 2Δ0, where Δ0 is its on-shell value. We find Δ0≃40MeV close to the chiral phase transition.

Ultralow-temperature heat transport in the quantum spin liquid candidate Ca10Cr7O28 with a bilayer kagome lattice

Recently, a novel material with a bilayer kagome lattice ${\mathrm{Ca}}_{10}{\mathrm{Cr}}_{7}{\mathrm{O}}_{28}$ was proposed to be a gapless quantum spin liquid, due to the lack of long-range magnetic order and the observation of broad diffuse excitations. Here, we present the ultralow-temperature thermal conductivity measurements on single crystals of ${\mathrm{Ca}}_{10}{\mathrm{Cr}}_{7}{\mathrm{O}}_{28}$ to detect its low-lying magnetic excitations. At finite temperatures, with increasing magnetic fields, the thermal conductivity exhibits a clear dip around 6 T, which may correspond to a crossover in the magnetic ground state. At the zero-temperature limit, no residual linear term is found at any fields, indicating the absence of gapless itinerant fermionic excitations. Therefore, if the spinons do exist, they are either localized or gapped. In the gapped case, the fitting of our data gives a small gap, $\mathrm{\ensuremath{\Delta}}\ensuremath{\sim}0.27(2)$ K. These results put strong constraints on the theoretical description of the ground state in this quantum spin liquid candidate.

Nonperturbative study of dynamical SUSY breaking in N=(2,2) Yang-Mills theory

We examine the possibility of dynamical supersymmetry breaking in two-dimensional $\mathcal{N} = (2, 2)$ supersymmetric Yang-Mills theory. The theory is discretized on a Euclidean spacetime lattice using a supersymmetric lattice action. We compute the vacuum energy of the theory at finite temperature and take the zero temperature limit. Supersymmetry will be spontaneously broken in this theory if the measured ground state energy is non-zero. By performing simulations on a range of lattices up to $96 \times 96$ we are able to perform a careful extrapolation to the continuum limit for a wide range of temperatures. Subsequent extrapolations to the zero temperature limit yield an upper bound on the ground state energy density. We find the energy density to be statistically consistent with zero in agreement with the absence of dynamical supersymmetry breaking in this theory.

Vortex nucleation limited mobility of free electron bubbles in the Gross-Pitaevskii model of a superfluid

We study the motion of an electron bubble in the zero temperature limit where neither phonons nor rotons provide a significant contribution to the drag exerted on an ion moving within the superfluid. By using the Gross-Clark model, in which a Gross-Pitaevskii equation for the superfluid wavefunction is coupled to a Schr\"{o}dinger equation for the electron wavefunction, we study how vortex nucleation affects the measured drift velocity of the ion. We use parameters that give realistic values of the ratio of the radius of the bubble with respect to the healing length in superfluid $^4$He at a pressure of one bar. By performing fully 3D spatio-temporal simulations of the superfluid coupled to an electron, that is modelled within an adiabatic approximation and moving under the influence of an applied electric field, we are able to recover the key dynamics of the ion-vortex interactions that arise and the subsequent ion-vortex complexes that can form. Using the numerically computed drift velocity of the ion as a function of the applied electric field, we determine the vortex-nucleation limited mobility of the ion to recover values in reasonable agreement with measured data.

Investigation of the open-circuit voltage in wide-bandgap InGaP-host InP quantum dot intermediate-band solar cells

To analyze the open-circuit voltage (Voc) in intermediate-band solar cells, we investigated the current–voltage characteristics in wide-bandgap InGaP-based InP quantum dot (QD) solar cells. From the temperature dependence of the current–voltage curves, we show that the Voc in InP QD solar cells increases with decreasing temperature. We use a simple diode model to extract Voc at the zero-temperature limit, V0, and the temperature coefficient C of the solar cells. Our results show that, while the C of InP QD solar cells is slightly larger than that of the reference InGaP solar cells, V0 significantly decreases and coincides with the bandgap energy of the InP QDs rather than that of the InGaP host. This V0 indicates that the Voc reduction in the InP QD solar cells is primarily caused by the breaking of the Fermi energy separation between the QDs and the host semiconductor in intermediate-band solar cells, rather than by enhanced carrier recombination.

Effect of quantum fluctuations in the high-energy cold nuclear equation of state and in compact star observables

We present a novel technique to obtain exact equation of state (EoS) by the Functional Renormalization Group (FRG) method, using the expansion of the effective potential in a base of harmonic functions at finite chemical potential. Within this theoretical framework we determined the equation of state and the phase diagram of a simple model of massless fermions coupled to scalars through Yukawa-coupling at the zero-temperature limit. We compared our results to the 1-loop and the mean field approximation of the same model and other high-density nuclear matter equation of states. We found a $10-20\%$ difference between these approximations. As an application, we used our exact, FRG-based equation of states to test the effect of the quantum fluctuations in superdense nuclear matter of a compact astrophysical object for the first time. We calculated the mass-radius relation for a compact star using the Tolmann-Oppenheimer-Volkov equation and observed a $\sim 5\%$ effect in compact star observables due to quantum fluctuations.

Metrologically useful states of spin-1 Bose condensates with macroscopic magnetization

We study theoretically the usefulness of spin-1 Bose condensates with macroscopic magnetization in a homogeneous magnetic field for quantum metrology. We demonstrate Heisenberg scaling of the quantum Fisher information for states in thermal equilibrium. The scaling applies to both antiferromagnetic and ferromagnetic interactions. The effect preserves as long as fluctuations of magnetization are sufficiently small. Scaling of the quantum Fisher information with the total particle number is derived within the mean-field approach in the zero temperature limit and exactly in the high magnetic field limit for any temperature. The precision gain is intuitively explained owing to subtle features of the quasi-distribution function in phase space.

Gauge-field model of superfluid turbulence in the zero-temperature limit

We present a gauge-field extension of the Bose condensate model that describes superfluid turbulence generated by the macroscopic motion of the superfluid. We first establish that the condensate model is dual to the short-range interacting loop gas model, wherein the loops represent quantum vortex lines. Vortex lines form, interact and proliferate as a result of the superfluid motion. Our extension is based on incorporating the Biot–Savart interaction between vortex lines, which is lacking in the loop gas model. We show that the extended loop gas is dual to a Ginzburg–Landau model, wherein the gauge coupling is between the macroscopic velocity field of the superfluid and the condensate. Applying the model to cylindrical and pipe flows, we describe how turbulence transitions with and without intermediate vortex flow, respectively.

Anomalous glassy dynamics in simple models of dense biological tissue

In order to understand the mechanisms for glassy dynamics in biological tissues and shed light on those in non-biological materials, we study the low-temperature disordered phase of 2D vertex-like models. Recently it has been noted that vertex models have quite unusual behavior in the zero-temperature limit, with rigidity transitions that are controlled by residual stresses and therefore exhibit very different scaling and phenomenology compared to particulate systems. Here we investigate the finite-temperature phase of two-dimensional Voronoi and Vertex models, and show that they have highly unusual, sub-Arrhenius scaling of dynamics with temperature. We connect the anomalous glassy dynamics to features of the potential energy landscape associated with zero-temperature inherent states.

Improved belief propagation algorithm finds many Bethe states in the random-field Ising model on random graphs.

We first present an empirical study of the Belief Propagation (BP) algorithm, when run on the random field Ising model defined on random regular graphs in the zero temperature limit. We introduce the notion of extremal solutions for the BP equations, and we use them to fix a fraction of spins in their ground state configuration. At the phase transition point the fraction of unconstrained spins percolates and their number diverges with the system size. This in turn makes the associated optimization problem highly non trivial in the critical region. Using the bounds on the BP messages provided by the extremal solutions we design a new and very easy to implement BP scheme which is able to output a large number of stable fixed points. On one hand this new algorithm is able to provide the minimum energy configuration with high probability in a competitive time. On the other hand we found that the number of fixed points of the BP algorithm grows with the system size in the critical region. This unexpected feature poses new relevant questions about the physics of this class of models.

Mutual friction in superfluid He−B3 in the low-temperature regime

We measure the response of a rotating sample of superfluid $^3$He-B to spin-down to rest in the zero-temperature limit. Deviations from perfect cylindrical symmetry in the flow environment cause the initial response to become turbulent. The remaining high polarization of vortices along the rotation axis suppresses the turbulent behavior and leads to laminar late-time response. We determine the dissipation during laminar decay at $(0.13-0.22) T_{\mathrm{c}}$ from the precession frequency of the remnant vortex cluster. We extract the mutual friction parameter $\alpha$ and confirm that its dependence on temperature and pressure agrees with theoretical predictions. We find that the zero-temperature extrapolation of $\alpha$ has pressure-independent value $\alpha(T=0) \sim 5 \cdot 10^{-4}$, which we attribute to a process where Kelvin waves, excited at surfaces of the container, propagate into the bulk and enhance energy dissipation via overheating vortex core-bound fermions.

Ergodic optimization in dynamical systems

Ergodic optimization is the study of problems relating to maximizing orbits and invariant measures, and maximum ergodic averages. An orbit of a dynamical system is called$f$-maximizing if the time average of the real-valued function$f$along the orbit is larger than along all other orbits, and an invariant probability measure is called$f$-maximizing if it gives$f$a larger space average than any other invariant probability measure. In this paper, we consider the main strands of ergodic optimization, beginning with an influential model problem, and the interpretation of ergodic optimization as the zero temperature limit of thermodynamic formalism. We describe typical properties of maximizing measures for various spaces of functions, the key tool of adding a coboundary so as to reveal properties of these measures, as well as certain classes of functions where the maximizing measure is known to be Sturmian.