Equilibrium Partition Function Research Articles

Ideal fracton superfluids

We investigate the thermodynamics of equilibrium thermal states and their near-equilibrium dynamics in systems with fractonic symmetries in arbitrary curved space. By explicitly gauging the fracton algebra we obtain the geometry and gauge fields that field theories with conserved dipole moment couple to. We use the resultant fracton geometry to show that it is not possible to construct an equilibrium partition function for global thermal states unless part of the fractonic symmetries is spontaneously broken. This leads us to introduce two classes of fracton superfluids with conserved energy and momentum, namely pp-wave and ss-wave fracton superfluids. The latter phase is an Aristotelian superfluid at ideal order but with a velocity constraint and can be split into two separate regimes: The U(1) fracton superfluid and the pinned ss-wave superfluid regimes. For each of these classes and regimes we formulate a hydrodynamic expansion and study the resultant modes. We find distinctive features of each of these phases and regimes at ideal order in gradients, without introducing dissipative effects. In particular we note the appearance of a sound mode for ss-wave fracton superfluids. We show that previous work on fracton hydrodynamics falls into these classes. Finally, we study ultra-dense pp-wave fracton superfluids with a large kinetic mass in addition to studying the thermodynamics of ideal Aristotelian superfluids.

Effects of single-point mutations on translocation of non-interacting heteropolymer protein chains

We analyse the role of single-point mutations on the translocation of heteropolymer protein chains with helical folding. We propose a statistical mechanics model that computes the equilibrium partition function of a given protein by incorporating experimental helix propensities of amino acids. From that we evaluate the free energy barrier for translocation and the average translocation time for single-point protein mutants and compared with wild-type proteins used as reference. In our calculations, single-point mutations that increase energy of the folded state in increase the energy barrier for translocation up to , , in consequence, the translocation time undergoes variations between and with the largest variations associated to substitutions of amino acids glycine and proline by alanine. In fact, substitutions of amino acids with the lowest helix propensities by amino acids with the largest helix propensities induced the largest mutational effects. These results indicate that effects of single-point mutations become evident when mutations increase energy of the folded state at least in . Our model predicts translocation time delays for proline to alanine single-point mutations which agree with deficiencies of protein translocation observed recently in experiments.

Thermodynamic properties of diatomic CO, CN, C2 and CO+ in CO2-N2 plasmas

The reliable data of plasma thermodynamic properties are of vital significance for aerodynamic modelling and plasma dynamics simulation. In this work, we have thoroughly evaluated the thermodynamic properties of diatomic CO, CN, C2 and CO+ by making use of a more rigorous approach. The internal energy levels were precisely determined by solving rotational dependence of the radial Schrödinger equation over a set of potential curves. The RKR method was used to generate the low-lying potential curves, while the ab initio results reported by the recent publications were selected for the potential curves of high-lying states. More electronic states were considered in this work than in previous publications, which helps to make the calculated results more accurate at high temperatures. The predicted results were verified by the available values in the recent studies and the relative deviations were systematically evaluated. The maximum relative difference of the equilibrium partition function is less than 7.7% for all species and not larger than 15.3% for equilibrium dimensionless specific heat.

Anomalous transport from equilibrium partition functions

We summarize recent advances in the application of the equilibrium partition function formalism for the study of the transport coefficients of relativistic fluids induced by quantum anomalies, at first and second order in the hydrodynamic expansion. We provide results for theories with Abelian and non-Abelian chiral fermions, and discuss some features of the corresponding constitutive relations.

Nonadiabatic instanton rate theory beyond the golden-rule limit.

Fermi's golden rule (GR) describes the leading-order behavior of the reaction rate as a function of the diabatic coupling. Its asymptotic (ℏ → 0) limit is the semiclassical golden-rule instanton rate theory, which rigorously approximates nuclear quantum effects, lends itself to efficient numerical computation, and gives physical insight into reaction mechanisms. However, the golden rule by itself becomes insufficient as the strength of the diabatic coupling increases, so higher-order terms must be additionally considered. In this work, we give a first-principles derivation of the next-order term beyond the golden rule, represented as a sum of three components. Two of them lead to new instanton pathways that extend the GR case and, among other factors, account for effects of recrossing on the full rate. The remaining component derives from the equilibrium partition function and accounts for changes in potential energy around the reactant and product wells due to diabatic coupling. The new semiclassical theory demands little computational effort beyond a GR instanton calculation. It makes it possible to rigorously assess the accuracy of the GR approximation and sets the stage for future work on general semiclassical nonadiabatic rate theories.

On Nieh-Yan transport

We study nondissipative transport induced by the Nieh-Yan anomaly. After computing the torsional terms in the equilibrium partition function using transgression, we find the constitutive relations for the covariant axial-vector, heat, stress, and spin currents. A number of new transport effects are found, driven by background torsion and the spin chemical potential. Torsional constitutive relations in two-dimensional systems are also analyzed.

Relativistic hydrodynamics with the parity anomaly

We consider the hydrodynamic regime of a 2+1 dimensions QFT with the parity anomaly. Beyond the known constraints from positivity of entropy production, we show that the anomaly inflow mechanism, from a corresponding bulk SPT phase, together with thermodynamic consistency of equilibrium partition functions, restricts the form of non-dissipative transport coefficients. This included the known form of quantised Hall conductivity, which is fixed to be σxy = e2/2h, along with new constraints on other three non-dissipative parity-odd transport coefficients.

Chiral torsional effects in anomalous fluids in thermal equilibrium

Using the similarity between spacetime torsion and axial gauge couplings, we study torsional contributions to the equilibrium partition function in a stationary background. In the case of a charged fluid minimally coupled to torsion, we spot the existence of linear torsional magnetic and vortical effects, while the axial-vector current and the spin energy potential do not receive corrections in the torsion at linear order. The covariant energy-momentum tensor, on the other hand, does contain terms linear in the torsion tensor. The case of a two-flavor hadronic superfluid is also analyzed, and the torsional contributions to the constitutive relations computed. Our results show the existence of a torsional electric chiral effect mediated by the charged pions.

Entanglement View of Dynamical Quantum Phase Transitions.

The analogy between an equilibrium partition function and the return probability in many-body unitary dynamics has led to the concept of dynamical quantum phase transition (DQPT). DQPTs are defined by nonanalyticities in the return amplitude and are present in many models. In some cases, DQPTs can be related to equilibrium concepts, such as order parameters, yet their universal description is an open question. In this Letter, we provide first steps toward a classification of DQPTs by using a matrix product state description of unitary dynamics in the thermodynamic limit. This allows us to distinguish the two limiting cases of "precession" and "entanglement" DQPTs, which are illustrated using an analytical description in the quantum Ising model. While precession DQPTs are characterized by a large entanglement gap and are semiclassical in their nature, entanglement DQPTs occur near avoided crossings in the entanglement spectrum and can be distinguished by a complex pattern of nonlocal correlations. We demonstrate the existence of precession and entanglement DQPTs beyond Ising models, discuss observables that can distinguish them, and relate their interplay to complex DQPT phenomenology.

Numerical method for computing the free energy of glasses.

We propose a numerical technique to compute the equilibrium free energy of glasses that cannot be prepared quasireversibly. For such systems, standard techniques for estimating the free energy by extrapolation cannot be used. Instead, we use a procedure that samples the equilibrium partition function of the basins of attraction of the different inherent structures (local potential energy minima) of the system. If all relevant inherent structures could be adequately sampled in the (supercooled) liquid phase, our approach would be rigorous. In any finite simulation, we will miss the lower-energy inherent structures that become dominant at very low temperatures. We find that our free energy estimates for a Kob-Andersen glass are lower than those obtained by very slow cooling, even at temperatures down to one-third of the glass transition temperature. The current approach could be applied to compute the chemical potential of ultrastable glassy materials and should enable the estimation of their solubility.

Anomalous currents and constitutive relations of a chiral hadronic superfluid

The anomalous currents of two-flavor chiral nuclear matter in the presence of chiral imbalance are computed, using recently developed methods exploiting generalized transgression, which facilitates the evaluation of both the equilibrium partition function and the covariant currents. The constitutive relations for both the broken and unbroken phase of the theory are studied and the out-of-equilibrium nondissipative transport coefficients determined. In the superfluid phase, the vector covariant currents exhibit nondissipative chiral electric, magnetic, and vortical effects, the latter governed by chiral imbalance.

Partition function for a mass dimension one fermionic field and the dark matter halo of galaxies

This work studies the finite temperature effects of a mass dimension one fermionic field, sometimes called Elko field. The equilibrium partition function was calculated by means of the imaginary time formalism and the result obtained was the same for a Dirac fermionic field, even though the Elko field does not satisfy a Dirac-like equation. The high and low temperature limits were obtained, and for the last case the degeneracy pressure due to Pauli exclusion principle can be responsible for the dark matter halos around galaxies to be greater than or of the same order of the galaxy radius. Also, for a light particle of about 1.0 eV and a density of just 1 particle per cubic centimeter, the value of the total dark matter mass due to Elko particles is of the same order of a typical galaxy. Such a result satisfactorily explains the dark matter as being formed just by Elko fermionic particles and also the existence of galactic halos that go beyond the observable limit.

Non-Abelian anomalous (super)fluids in thermal equilibrium from differential geometry

We apply differential geometry methods to the computation of the anomaly-induced hydrodynamic equilibrium partition function. Implementing the imaginary-time prescription on the Chern-Simons effective action on a stationary background, we obtain general closed expressions for both the invariant and anomalous part of the partition function. This is applied to the Wess-Zumino-Witten action for Goldstone modes, giving the equilibrium partition function of superfluids. In all cases, we also study the anomaly-induced gauge currents and energy-momentum tensor, providing explicit expressions for them.

Role of single-point mutations and deletions on transition temperatures in ideal proteinogenic heteropolymer chains in the gas phase.

A coarse-grained statistical mechanics-based model for ideal heteropolymer proteinogenic chains of non-interacting residues is presented in terms of the size K of the chain and the set of helical propensities [Formula: see text] associated with each residue j along the chain. For this model, we provide an algorithm to compute the degeneracy tensor [Formula: see text] associated with energy level [Formula: see text] where [Formula: see text] is the number of residues with a native contact in a given conformation. From these results, we calculate the equilibrium partition function [Formula: see text] and characteristic temperature [Formula: see text] at which a transition from a low to a high entropy states is observed. The formalism is applied to analyze the effect on characteristic temperatures [Formula: see text] of single-point mutations and deletions of specific amino acids [Formula: see text] along the chain. Two probe systems are considered. First, we address the case of a random heteropolymer of size K and given helical propensities [Formula: see text] on a conformational phase space. Second, we focus our attention to a particular set of neuropentapeptides, [Met-5] and [Leu-5] enkephalins whose thermodynamic stability is a key feature on their coupling to [Formula: see text] and [Formula: see text] receptors and the triggering of biochemical responses.

Equilibrium partition function for nonrelativistic fluids

We construct an equilibrium partition function for a nonrelativistic fluid and use it to constrain the dynamics of the system. The construction is based on light cone reduction, which is known to reduce the Poincar\'e symmetry to Galilean in one lower dimension. We modify the constitutive relations of a relativistic fluid, and find that its symmetry broken phase---``null fluid'' is equivalent to the nonrelativistic fluid. In particular, their symmetries, thermodynamics, constitutive relations, and equilibrium partition function match exactly to all orders in derivative expansion.

Effective actions for relativistic fluids from holography

Motivated by recent progress in developing action formulations of relativistic hydrodynamics, we use holography to derive the low energy dissipationless effective action for strongly coupled conformal fluids. Our analysis is based on the study of novel double Dirichlet problems for the gravitational field, in which the boundary conditions are set on two codimension one timelike hypersurfaces (branes). We provide a geometric interpretation of the Goldstone bosons appearing in such constructions in terms of a family of spatial geodesics extending between the ultraviolet and the infrared brane. Furthermore, we discuss supplementing double Dirichlet problems with information about the near-horizon geometry. We show that upon coupling to a membrane paradigm boundary condition, our approach reproduces correctly the complex dispersion relation for both sound and shear waves. We also demonstrate that upon a Wick rotation, our formulation reproduces the equilibrium partition function formalism, provided the near-horizon geometry is properly accounted for. Finally, we define the conserved hydrodynamic entropy current as the Noether current associated with a particular transformation of the Goldstone bosons.

Torsional response of relativistic fermions in 2 + 1 dimensions

We consider the equilibrium partition function of an ideal gas of Dirac fermions minimally coupled to torsion in $2+1$ dimensions. We show that the energy-momentum tensor reproduces the Hall viscosity and other parity violating terms of first order in the torsion. We also consider the modifications of the constitutive relations, and classify the corresponding susceptibilities. An entropy current consistent with zero production of entropy in equilibrium is constructed.

Thermal Hall effect and geometry with torsion.

We formulate a geometric framework that allows us to study momentum and energy transport in nonrelativistic systems. It amounts to a coupling of the nonrelativistic system to the Newton-Cartan (NC) geometry with torsion. The approach generalizes the classic Luttinger's formulation of thermal transport. In particular, we clarify the geometric meaning of the fields conjugated to energy and energy current. These fields describe the geometric background with nonvanishing temporal torsion. We use the developed formalism to construct the equilibrium partition function of a nonrelativistic system coupled to the NC geometry in 2+1 dimensions and to derive various thermodynamic relations.

(Non)-dissipative hydrodynamics on embedded surfaces

We construct the theory of dissipative hydrodynamics of uncharged fluids living on embedded space-time surfaces to first order in a derivative expansion in the case of codimension-1 surfaces (including fluid membranes) and the theory of non-dissipative hydrodynamics to second order in a derivative expansion in the case of codimension higher than one under the assumption of no angular momenta in transverse directions to the surface. This construction includes the elastic degrees of freedom, and hence the corresponding transport coefficients, that take into account transverse fluctuations of the geometry where the fluid lives. Requiring the second law of thermodynamics to be satisfied leads us to conclude that in the case of codimension-1 surfaces the stress-energy tensor is characterized by 2 hydrodynamic and 1 elastic independent transport coefficient to first order in the expansion while for codimension higher than one, and for non-dissipative flows, the stress-energy tensor is characterized by 7 hydrodynamic and 3 elastic independent transport coefficients to second order in the expansion. Furthermore, the constraints imposed between the stress-energy tensor, the bending moment and the entropy current of the fluid by these extra non-dissipative contributions are fully captured by equilibrium partition functions. This analysis constrains the Young modulus which can be measured from gravity by elastically perturbing black branes.

Entropy current and equilibrium partition function in fluid dynamics

Existence of an entropy current with non-negative divergence puts a lot of constraints on the transport coefficients of a fluid, so does the existence of equilibrium. In all the cases we have studied so far we have seen an overlap between these two sets of constraints. In this note we shall try to explore the reason for such an overlap. We shall also see how a part of the entropy current could be determined from the equilibrium partition function.