Microscopic Formula Research Articles

Entropy associated with conformational and solvent-density fluctuations in biomolecular solutions

Microscopic formula to describe the entropy of biomolecular solutions are derived based on the Gibbs formula of entropy, and the generalized Langevin theory combined with the RISM/3D-RISM theory. Two formula are derived: one is concerned with the conformational fluctuation of a biomolecule, and the other with the density fluctuation of solvent around a solute. The formula derived for the entropy associated with the conformational fluctuation is Sconf=12kBlog2π3NA+3N2kBwhere N is the number of atoms in the solute, and A is the determinant of the inverse of the variance–covariance matrix of conformational fluctuation.The formula for the entropy of solvent at a pair of positions around a solute is also derived to be, ssolv(r,r′)=12kBlog2πnB+3n2kBwhere n is the number of atoms in a solvent molecule, and B is essentially the determinant of the matrix of the density-pair-correlation functions. The entropy at a local position r may be obtained by integrating the expression by r′ over the entire volume of the system.The feasibility of the calculation to find the entropies is discussed.

Chirality-Induced Phonon-Spin Conversion at an Interface.

We consider spin injection driven by nonequilibrium chiral phonons from a chiral insulator into an adjacent metal. Phonon-spin conversion arises from the coupling of the electron spin with the microrotation associated with chiral phonons. We derive a microscopic formula for the spin injection rate at a metal-insulator interface. Our results clearly illustrate the microscopic origin of spin current generation by chiral phonons and may lead to a breakthrough in the development of spintronic devices without heavy elements.

Lieb-Schultz-Mattis anomalies as obstructions to gauging (non-on-site) symmetries

We study ’t Hooft anomalies of global symmetries in 1+1d lattice Hamiltonian systems. We consider anomalies in internal and lattice translation symmetries. We derive a microscopic formula for the “anomaly cocycle” using topological defects implementing twisted boundary conditions. The anomaly takes value in the cohomology group H^3(G,U(1)) × H^2(G,U(1))H3(G,U(1))×H2(G,U(1)). The first factor captures the anomaly in the internal symmetry group G, and the second factor corresponds to a generalized Lieb-Schultz-Mattis anomaly involving G and lattice translation. We present a systematic procedure to gauge internal symmetries (that may not act on-site) on the lattice. We show that the anomaly cocycle is the obstruction to gauging the internal symmetry while preserving the lattice translation symmetry. As an application, we construct anomaly-free chiral lattice gauge theories. We demonstrate a one-to-one correspondence between (locality-preserving) symmetry operators and topological defects, which is essential for the results we prove. We also discuss the generalization to fermionic theories. Finally, we construct non-invertible lattice translation symmetries by gauging internal symmetries with a Lieb-Schultz-Mattis anomaly.

General theory of the viscosity of liquids and solids from nonaffine particle motions.

A microscopic formula for the viscosity of liquids and solids is derived rigorously from a first-principles (microscopically reversible) Hamiltonian for particle-bath atomistic motion. The derivation is done within the framework of nonaffine linear response theory. This formula may lead to a valid alternative to the Green-Kubo approach to describe the viscosity of condensed matter systems from molecular simulations without having to fit long-time tails. Furthermore, it provides a direct link between the viscosity, the vibrational density of states of the system, and the zero-frequency limit of the memory kernel. Finally, it provides a microscopic solution to Maxwell's interpolation problem of viscoelasticity by naturally recovering Newton's law of viscous flow and Hooke's law of elastic solids in two opposite limits.

Predictive power of theoretical models in cluster radioactivity

Many microscopic and macroscopic models are available in the literature to study the cluster radioactivity. The investigation of appropriate theoretical model to study the cluster decay process is an important aspect. We studied cluster-decay in the atomic and mass number range [Formula: see text] and [Formula: see text] using modified generalized liquid drop model (MGLDM), Coulomb and proximity potential model (CPPM) and generalized liquid drop model (GLDM). The results obtained using macroscopic models are compared with that of microscopic models. There are various mass excess tables available in the literature. But indentification of suitable mass excess table for cluster radioactivity is an also important part of this study. The macroscopic models, such as MGLDM, CPPM and GLDM, were used to analyze cluster-decay half-lives. Along with this, microscopic and semi-empirical relations were also investigated. The standard deviation is evaluated in macroscopic, microscopic and semi-empirical formulae. A detailed investigation shows that among macroscopic model-MGLDM, macroscopic-RMFM and in case of semi-empirical formulae, AZF produces less deviation. Hence, these results give an insight into prediction of cluster decay half-lives in heavy and superheavy region for unknown nuclei.

Rotating black holes and exotic compact objects in the Kerr/CFT correspondence within Rastall gravity

Quantum gravitational effects on the near horizon may alter the black hole's horizon drastically to be partially reflective, portrayed by a quantum membrane. With this modification, the object can be considered as an exotic compact object (ECO). Quantum effects on the strong gravitational regime may also lead to a non-conserved matter tensor that can be described phenomenologically using Rastall gravity. In this work, we study the properties of black holes and ECOs within Rastall gravity using Kerr/CFT correspondence. We systematically investigate the properties of the most general rotating black hole solutions in Rastall gravity, i.e., Kerr-Newman-NUT-Kiselev, and reveal its hidden conformal symmetry. The Cardy microscopic entropy formula and absorption cross-sections from 2D CFT are computed and then matched with gravity calculation. We also extend the dual CFT analysis for studying the properties of ECOs. The existence of the quantum membrane leads to the appearance of the gravitational echoes that is manifested as an oscillatory feature on the absorption cross-section. We compute the absorption cross-section and quasi-normal modes in the dual CFT picture. We also compare the absorption cross-section of ECOs to that of black holes. We find that the Rastall coupling constant plays a significant role for both objects. We also obtain that the echo time delay depends explicitly on the Rastall coupling constant. This coupling constant may play a role to recover the correction on time delay that is believed as a non-linear physics effect. Henceforth, the signature of the Rastall gravity can be probed from the time-delay observation.

The fuzzball hair removal

The gravitational description of black hole microstructure via the fuzzball proposal suggests a vast space of solutions called fuzzballs. This idea together with the 4d and 5d microscopic counting formulas necessitates that each supersymmetric 4d fuzzball admits an infinite number of hair. The hair removed fuzzballs are the true horizon degrees of freedom. We discuss how to construct/identify, count, and remove fuzzball hair.

Microscopic formulas for thermoelectric transport coefficients in lattice systems

A macroscopic description of thermoelectric phenomena involves several tensorial transport coefficients. Textbook microscopic Kubo formulas for them are plagued with ambiguities in the definitions of the current operators and the magnetization. We derive a version of these formulas for lattice systems which is free from ambiguities but contains additional terms compared to the textbook results. For symmetric components of thermoelectric tensors, we identify a large class of lattice systems for which the additional terms vanish with a natural choice of the energy current. To eliminate ambiguities in the skew-symmetric components, one needs to interpret them as relative quantities: only their differences for pairs of materials are well-defined.

Improved macroscopic microscopic mass formula

A nuclear mass formula based on the macroscopic microscopic approach is proposed, in which the number of model parameters is reduced compared with other macroscopic microscopic models. The root mean square (RMS) deviation with respect to 2314 training sets (measured nuclear masses) is reduced to 0.447 MeV, and the calculated value of each nucleus is no more than 0.8% different from the experimental value. The single and two nucleon separation energies and the shell gaps are calculated to test the model. The shell corrections and double magic number of superheavy nuclei are also analyzed.

Pancharatnam metals with integer and fractional quantum Hall effects

ABSTRACT Weakly interacting Fermi liquid can exhibit integer or fractional quantum Hall effect at sufficiently low temperatures, and in the presence of variable applied magnetic and/or electric fields. The said effects have been captured only incompletely by means of the Klitzing conductance formula, multiplied by the dimensionless filling factor (integer or fractional), ν because scattering rate cannot be absent for any conductor that is neither a perfect conductor at zero Kelvin (in the absence of phonons, scattering rate, Cooper pairing and Meissner effect) nor a superconductor. Here, we shall derive the proper microscopic resistance formula based on the notion of Pancharatnam phase retardation that captures both integer and fractional quantum Hall effects. We then compute the Planck constant from the Pancharatnam resistance formula, as well as provide a formal proof for this new formula. We shall unambiguously elaborate why the Pancharatnam resistance formula gives the complete physics of electron transport phenomena responsible for the quantum Hall effects, which include the changes to longitudinal and Hall resistance, as well as the temperature effect.

Transport Properties in Magnetized Compact Stars

Transport properties of dense quark matter are discussed in the strong magnetic field, B. B dependence as well as density dependence of the Hall conductivity is discussed, based on the microscopic Kubo formula. We took into account the possibility of the inhomogeneous chiral phase at moderate densities, where anomalous Hall effect is intrinsic and resembles the one in Weyl semimetals in condensed matter physics. Some theoretical aspects inherent in anomalous Hall effect are also discussed.

Microscopic derivation of density functional theory for superfluid systems based on effective action formalism

Abstract A density-functional theory for superfluid systems is developed in the framework of the functional renormalization group based on the effective action formalism. We introduce the effective action for the particle-number and non-local pairing densities and demonstrate that the Hohenberg–Kohn theorem for superfluid systems is established in terms of the effective action. The flow equation for the effective action is then derived, where the flow parameter runs from $0$ to $1$, corresponding to the non-interacting and interacting systems. From the flow equation and the variational equation that the equilibrium density satisfies, we obtain the exact expression for the Kohn–Sham potential generalized to include the pairing potentials. The resultant Kohn–Sham potential has a nice feature in that it expresses the microscopic formulae of the external, Hartree, pairing and exchange–correlation terms separately. It is shown that our Kohn–Sham potential gives the ground-state energy of the Hartree–Fock–Bogoliubov theory by neglecting the correlations. An advantage of our exact formalism lies in the fact that it provides ways to improve the correlation part systematically.

Systematic study of the α decay preformation factors of the nuclei around the Z = 82, N = 126 shell closures within the generalized liquid drop model * * Supported in part by the National Natural Science Foundation of China (11205083, 11505100, 11705055), the Construct Program of the Key Discipline in Hunan Province, the Research Foundation of Education Bureau of

In this study, we systematically investigate the decay preformation factors, , and the decay half-lives of 152 nuclei around Z = 82, N = 126 closed shells based on the generalized liquid drop model (GLDM) with being extracted from the ratio of the calculated decay half-life to the experimental one. The results show that there is a remarkable linear relationship between and the product of valance protons (holes) and valance neutrons (holes) . At the same time, we extract the decay preformation factor values of the even–even nuclei around the Z = 82, N = 126 closed shells from the study of Sun [J. Phys. G: Nucl. Part. Phys., 45: 075106 (2018)], in which the decay was calculated by two different microscopic formulas. We find that the decay preformation factors are also related to . Combining with our previous studies [Sun , Phys. Rev. C, 94: 024338 (2016); Deng , ibid. 96: 024318 (2017); Deng , ibid. 97: 044322 (2018)] and that of Seif [Phys. Rev. C, 84: 064608 (2011)], we suspect that this phenomenon of linear relationship for the nuclei around the above closed shells is model-independent. This may be caused by the effect of the valence protons (holes) and valence neutrons (holes) around the shell closures. Finally, using the formula obtained by fitting the decay preformation factor data calculated by the GLDM, we calculate the decay half-lives of these nuclei. The calculated results agree with the experimental data well.

Quantum mechanism of condensation and high Tc superconductivity

The main objective of this paper is to introduce a new quantum mechanism of condensates and superconductivity based on a new interpretation of quantum mechanical wavefunctions, and on recent developments in quantum physics and statistical physics. First, we postulate that the wavefunction [Formula: see text]e[Formula: see text] is the common wavefunction for all particles in the same class determined by the external potential V(x), [Formula: see text](x)[Formula: see text] represents the distribution density of the particles, and [Formula: see text] is the velocity field of the particles. Although the new interpretation does not alter the basic theories of quantum mechanics, it is an entirely different interpretation from the classical Bohr interpretation, removes all absurdities and offers new insights for quantum physics and for condensed matter physics. Second, we show that the key for condensation of bosonic particles is that their interaction is sufficiently weak to ensure that a large collection of boson particles are in a state governed by the same condensation wavefunction field [Formula: see text] under the same bounding potential V. For superconductivity, the formation of superconductivity comes down to conditions for the formation of electron pairs, and for the electron pairs to share a common wavefunction. Thanks to the recently developed principle of interaction dynamics (PID) interaction potential of electrons and the average-energy level formula of temperature, these conditions for superconductivity are explicitly derived. Furthermore, we obtain both microscopic and macroscopic formulas for the critical temperature. The field and topological phase transition equations for condensates are also derived.

Quantum black hole entropy, localization and the stringy exclusion principle

Supersymmetric localization has led to remarkable progress in computing quantum corrections to BPS black hole entropy. The program has been successful especially for computing perturbative corrections to the Bekenstein-Hawking area formula. In this work, we consider non-perturbative corrections related to polar states in the Rademacher expansion, which describes the entropy in the microcanonical ensemble. We propose that these non-perturbative effects can be identified with a new family of saddles in the localization of the quantum entropy path integral. We argue that these saddles, which are euclidean AdS2 × S1 × S2 geometries, arise after turning on singular fluxes in M-theory on a Calabi-Yau. They cease to exist after a certain amount of flux, resulting in a finite number of geometries; the bound on that number is in precise agreement with the stringy exclusion principle. Localization of supergravity on these backgrounds gives rise to a finite tail of Bessel functions in agreement with the Rademacher expansion. As a check of our proposal, we test our results against well known microscopic formulas for one-eighth and one-quarter BPS black holes in mathcal{N}=8 and mathcal{N}=4 string theory respectively, finding agreement. Our method breaks down precisely when mock-modular effects are expected in the entropy of one-quarter BPS dyons and we comment upon this. Furthermore, we mention possible applications of these results, including an exact formula for the entropy of four dimensional mathcal{N}=2 black holes.

Spatial distribution of superfluidity and superfluid distillation of Bose liquids

Under the assumption of two fluid kinematics of a nonrelativistic Bose liquid in the presence of a local velocity field $v(x)$, local Galilei transformations are used to derive formulas for the spatial distribution of superfluidity. The local formulation is shown to subsume several descriptions of superfluidity, from Landau's free quasiparticle picture of the normal fluid to the fully microscopic winding number formula for superfluid density. We derive the superfluid distribution of generic pure states of 1-d bosonic systems by using the continuum analog of matrix product states. With a view toward spatially structured superfluid-based quantum devices, we consider the limits to local distillation of superfluidity within the framework of localized resource theories of quantum coherence.

Spin transfer torques and spin-dependent transport in a metallic F/AF/N tunneling junction

We study spin-dependent electron transport through a ferromagnetic-antiferromagnetic-normal metal tunneling junction subject to a voltage or temperature bias, in the absence of spin-orbit coupling. We derive microscopic formulas for various types of spin torque acting on the antiferromagnet as well as for charge and spin currents flowing through the junction. The obtained results are applicable in the limit of slow magnetization dynamics. We identify a parameter regime in which an unconventional damping-like torque can become comparable in magnitude to the equivalent of the conventional Slonczewski's torque generalized to antiferromagnets. Moreover, we show that the antiferromagnetic sublattice structure opens up a channel of electron transport which does not have a ferromagnetic analogue and that this mechanism leads to a pronounced field-like torque. Both charge conductance and spin current transmission through the junction depend on the relative orientation of the ferromagnetic and the antiferromagnetic vectors (order parameters). The obtained formulas for charge and spin currents allow us to identify the microscopic mechanisms responsible for this angular dependence and to assess the efficiency of an antiferromagnetic metal acting as a spin current polarizer.

On exponentially suppressed corrections to BMPV black hole entropy

The microscopic formula for the degeneracy of BMPV black hole microstates contains a series of exponentially suppressed corrections to the leading Bekenstein Hawking expression. We identify saddle points of the quantum entropy function for the BMPV black hole which are natural counterparts to these corrections and discuss the matching of leading and next-to-leading terms from the microscopic and macroscopic sides in a limit where the black hole charges are large.

Exact Holography and Black Hole Entropy in mathcal{N}=8 and mathcal{N}=4 String Theory

We compute the exact entropy of one-eighth and one-quarter BPS black holes in mathcal{N}=8 and mathcal{N}=4 string theory respectively. This includes all the mathcal{N}=4 CHL models in both K3 and T4 compactifications. The main result is a measure for the finite dimensional integral that one obtains after localization of supergravity on AdS2× S2. This measure is determined entirely by an anomaly in supersymmetric Chern-Simons theory on local AdS3 and takes into account the contribution from all the supergravity multiplets. In Chern-Simons theory on compact manifolds, this is the anomaly that computes a certain one-loop dependence on the volume of the manifold. For one-eighth BPS black holes, our results are a first principles derivation of a measure proposed in arXiv:1111.1161, while in the case of one-quarter BPS black holes our result computes exactly all the perturbative or area corrections. Moreover, we argue that instantonic contributions can be incorporated and give evidence by computing the measure, which matches precisely the microscopics. Along with this, we find a unitary condition that truncates the answer to a finite sum of instantons in perfect agreement with a microscopic formula. Our results therefore solve a number of puzzles related to localization in supergravity and constitute a larger number of examples where holography can be shown to hold exactly.

Soft hairy horizons in three spacetime dimensions

We discuss some aspects of soft hairy black holes and a new kind of "soft hairy cosmologies", including a detailed derivation of the metric formulation, results on flat space, and novel observations concerning the entropy. Remarkably, like in the case with negative cosmological constant, we find that the asymptotic symmetries for locally flat spacetimes with a horizon are governed by infinite copies of the Heisenberg algebra that generate soft hair descendants. It is also shown that the generators of the three-dimensional Bondi-Metzner-Sachs algebra arise from composite operators of the affine u(1) currents through a twisted Sugawara-like construction. We then discuss entropy macroscopically, thermodynamically and microscopically and discover that a microscopic formula derived recently for boundary conditions associated to the Korteweg-de Vries hierarchy fits perfectly our results for entropy and ground state energy. We conclude with a comparison to related approaches.