Grand canonical partition function of a serial metallic island system

We present a calculation of the grand canonical partition function of a serial metallic island system by the imaginary-time path integral formalism. To this purpose, all electronic excitations in the lead and island electrodes are described using Grassmann numbers. The Coulomb charging energy of the system is represented in terms of phase fields conjugate to the island charges. By the large channel approximation, the tunneling action phase dependence can also be determined explicitly. Therefore, we represent the partition function as a path integral over phase fields with a path probability given in an analytically known effective action functional. Using the result, we also propose a calculation of the average electron number of the serial island system in terms of the expectation value of winding numbers. Finally, as an example, we describe the Coulomb blockade effect in the two-island system by the average electron number and propose a method to construct the quantum stability diagram.

Induced surface and curvature tension equation of state for hadron resonance gas in finite volumes and its relation to morphological thermodynamics

Here, we develop an original approach to investigate the grand canonical partition function of the multicomponent mixtures of Boltzmann particles with hard-core interaction in finite and even small systems of the volumes above 20 fm3. The derived expressions of the induced surface tension equation of state (EoS) are analyzed in detail. It is shown that the metastable states, which can emerge in the finite systems with realistic interaction, appear at very high pressures at which the hadron resonance gas, most probably, is not applicable at all. It is shown how and under what conditions the obtained results for finite systems can be generalized to include into a formalism the equation for curvature tension. The applicability range of the obtained equations of induced surface and curvature tensions for finite systems is discussed and their close relations to the equations of the morphological thermodynamics are established. The hadron resonance gas model on the basis of the obtained advanced EoS is worked out. Also, this model is applied to analyze the chemical freeze-out of hadrons and light nuclei with the number of (anti-) baryons not exceeding 4. Their multiplicities were measured by the ALICE Collaboration in the central lead–lead collisions at the center-of-mass energy [Formula: see text] TeV.

The topologically twisted index of $$ \mathcal{N} $$ = 4 SU(N) Super-Yang-Mills theory and a black hole Farey tail

We investigate the large-N asymptotics of the topologically twisted index of $$ \mathcal{N} $$ N = 4 SU(N) Super-Yang-Mills (SYM) theory on T2 × S2 and provide its holographic interpretation based on the black hole Farey tail [1]. In the field theory side, we use the Bethe-Ansatz (BA) formula, which gives the twisted index of $$ \mathcal{N} $$ N = 4 SYM theory as a discrete sum over Bethe vacua, to compute the large-N asymptotics of the twisted index. In a dual $$ \mathcal{N} $$ N = 2 gauged STU model, we construct a family of 5d extremal solutions uplifted from the 3d black hole Farey tail, and compute the regularized on-shell actions. The gravitational partition function given in terms of these regularized on-shell actions is then compared with a canonical partition function derived from the twisted index by the inverse Laplace transform, in the large-N limit. This extends the previous microstate counting of an AdS5 black string by the twisted index and thereby improves holographic understanding of the twisted index.

Microscopic entropy of AdS3 black holes revisited

We revisit the microscopic description of AdS3 black holes in light of recent progress on their higher dimensional analogues. The grand canonical partition function that follows from the AdS3/CFT2 correspondence describes BPS and nearBPS black hole thermodynamics. We formulate an entropy extremization principle that accounts for both the black hole entropy and a constraint on its charges, in close analogy with asymptotically AdS black holes in higher dimensions. We are led to interpret supersymmetric black holes as ensembles of BPS microstates satisfying a charge constraint that is not respected by individual states. This interpretation provides a microscopic understanding of the hitherto mysterious charge constraints satisfied by all BPS black holes in AdS. We also develop thermodynamics and a nAttractor mechanism of AdS3 black holes in the nearBPS regime.

Summing over geometries in string theory

We examine the question how string theory achieves a sum over bulk geometries with fixed asymptotic boundary conditions. We discuss this problem with the help of the tensionless string on $$ {\mathrm{\mathcal{M}}}_3\times {\mathrm{S}}^3\times {\mathbbm{T}}^4 $$ ℳ 3 × S 3 × T 4 (with one unit of NS-NS flux) that was recently understood to be dual to the symmetric orbifold SymN ($$ {\mathbbm{T}}^4 $$ T 4 ). We strengthen the analysis of [1] and show that the perturbative string partition function around a fixed bulk background already includes a sum over semi-classical geometries and large stringy corrections can be interpreted as various semi-classical geometries. We argue in particular that the string partition function on a Euclidean wormhole geometry factorizes completely into factors associated to the two boundaries of spacetime. Central to this is the remarkable property of the moduli space integral of string theory to localize on covering spaces of the conformal boundary of ℳ3. We also emphasize the fact that string perturbation theory computes the grand canonical partition function of the family of theories ⊕N SymN ($$ {\mathbbm{T}}^4 $$ T 4 ). The boundary partition function is naturally expressed as a sum over winding worldsheets, each of which we interpret as a ‘stringy geometry’. We argue that the semi-classical bulk geometry can be understood as a condensate of such stringy geometries. We also briefly discuss the effect of ensemble averaging over the Narain moduli space of $$ {\mathbbm{T}}^4 $$ T 4 and of deforming away from the orbifold by the marginal deformation.

Harmonically confined Bose–Einstein condensation on the surface of a cylinder

It is well known that Bose–Einstein condensation cannot occur in a free two-dimensional (2D) system. Recently, several studies have showed that BEC can occur on the surface of a sphere. We investigate BEC on the surface of cylinder on both sides of which atoms are confined in a one-dimensional (1D) harmonic potential. In this work, only the non-interacting Bose gas is considered. We determine the critical temperature and the condensate fraction in the geometry using the semi-classical approximation. Moreover, the thermodynamic properties of ideal bosons are also studied using the grand canonical partition function.

The First Principle Approach in Estimating Bulk Modulus Based on Explicit Expression of Canonical Partition Function

The bulk modulus is one of the most important characteristic features of solids. Accordingly, we have developed a statistical-mechanical treatment based on an equation which enables us to calculate the bulk modulus for solids with the minimum manifold of input data. In our model, a conjunction between Gruneisen parameter and canonical partition function has been established. We have found out that the volume dependency of Gruneisen parameter is critical in estimating bulk modulus. The result for hexagonal closed- packed (hcp) iron is very good and commensurate with the best measurements. This framework can be extended to the other elemental solids or a variety of compounds.