Breakdown of the Wiedemann-Franz law in strongly-coupled electron-phonon system, application to the cuprates

With the superconducting cuprates in mind, a set of unitary transformations was used to decouple electrons and phonons in the strong-coupling limit. While phonons remain almost unrenormalised, electrons are transformed into itinerent singlet and triplet bipolarons and thermally excited polarons. The triplet/singlet exchange energy and the binding energy of the bipolarons are thought to account for the spin and charge pseudogaps in the cuprates, respectively. We calculated the Hall Lorenz number of the system to show that the Wiedemann-Franz law breaks down due to the interference of the polaron and bipolaron contributions to heat flow. The model provides a quantitative fit to magnetotransport data in the cuprates. Furthermore we are able to extract the phonon component of the thermal conductivity with the use of experimental data and the model. Our results further validate the use of a charged Bose gas model to describe normal and superconducting properties of unconventional superconductors.Comment: 9 pages, 6 figures. Submitted to Physical Review

Time-dependent backgrounds of 2D string theory: Non-perturbative effects

We study the non-perturbative corrections (NPC) to the partition function of a compactified 2D string theory in a time-dependent background generated by a tachyon source. The sine-Liouville deformation of the theory is a particular case of such a background. We calculate the leading as well as the subleading NPC using the dual description of the string theory as matrix quantum mechanics. As in the minimal string theories, the NPC are classified by the double points of a complex curve. We calculate them by two different methods: by solving Toda equation and by evaluating the quasiclassical fermion wave functions. We show that the result can be expressed in terms of correlation functions of the bosonic field associated with the tachyon source and identify the leading and the subleading corrections as the contributions from the one-point (disk) and two-point (annulus) correlation functions.Comment: 37 pages, 2 figure

Thermodynamics of 2D string theory

We calculate the free energy, energy and entropy in the matrix quantum mechanical formulation of 2D string theory in a background strongly perturbed by tachyons with the imaginary Minkowskian momentum $\pm i/R$ (``Sine-Liouville'' theory). The system shows a thermodynamical behaviour corresponding to the temperature $T=1/(2\pi R)$. We show that the microscopically calculated energy of the system satisfies the usual thermodynamical relations and leads to a non-zero entropy.Comment: 13 pages, lanlmac; typos correcte

On the total mean curvature of non-rigid surfaces

Using Green's theorem we reduce the variation of the total mean curvature of a smooth surface in the Euclidean 3-space to a line integral of a special vector field and obtain the following well-known theorem as an immediate consequence: the total mean curvature of a closed smooth surface in the Euclidean 3-space is stationary under an infinitesimal flex.Comment: 4 page

Polaron and bipolaron transport in a charge segregated state of doped strongly correlated 2D semiconductor

The 2D lattice gas model with competing short and long range interactions is appliedused for calculation of the incoherent charge transport in the classical strongly-correlated charge segregated polaronic state. We show, by means of Monte-Carlo simulations, that at high temperature the transport is dominated by hopping of the dissociated correlated polarons, where with thetheir mobility is inversely proportional to the temperature. At the temperatures below the clustering transition temperature the bipolaron transport becomes dominant. The energy barrier for the bipolaron hopping is determined by the Coulomb effects and is found to be lower than the barrier for the single-polaron hopping. This leads to drastically different temperature dependencies of mobilities for polarons and bipolarons at low temperatures

2D String Theory as Normal Matrix Model

We show that the $c=1$ bosonic string theory at finite temperature has two matrix-model realizations related by a kind of duality transformation. The first realization is the standard one given by the compactified matrix quantum mechanics in the inverted oscillator potential. The second realization, which we derive here, is given by the normal matrix model. Both matrix models exhibit the Toda integrable structure and are associated with two dual cycles (a compact and a non-compact one) of a complex curve with the topology of a sphere with two punctures. The equivalence of the two matrix models holds for an arbitrary tachyon perturbation and in all orders in the string coupling constant.Comment: lanlmac, 21 page

Vortex matter in the charged Bose liquid at absolute zero

The Gross-Pitaevskii-type equation is solved for the charge Bose liquid in the external magnetic field at zero temperature. There is a vortex lattice with locally broken charge neutrality. The boson density is modulated in real space and each vortex is charged. Remarkably, there is no upper critical field at zero temperature, so the density of single flux-quantum vortices monotonously increases with the magnetic field up to B=infinity and no indication of a phase transition. The size of each vortex core decreases as about 1/sqrt(B) keeping the system globally charge neutral. If bosons are composed of two fermions, a phase transition to a spin-polarized Fermi liquid at some magnetic field larger than the pair-breaking field is predicted.Comment: 4 pages, 4 figures, references update

Polarons in suspended carbon nanotubes

We prove theoretically the possibility of electric-field controlled polaron formation involving flexural (bending) modes in suspended carbon nanotubes. Upon increasing the field, the ground state of the system with a single extra electron undergoes a first order phase transition between an extended state and a localized polaron state. For a common experimental setup, the threshold electric field is only of order $\simeq 10^{-2}$ V/$\mu$m

Patterns in soft and biological matters

The issue is devoted to theoretical, computer and experimental studies of internal heterogeneous patterns, their morphology and evolution in various soft physical systems-organic and inorganic materials (e.g. alloys, polymers, cell cultures, biological tissues as well as metastable and composite materials). The importance of these studies is determined by the significant role of internal structures on the macroscopic properties and behaviour of natural and manufactured tissues and materials. Modern methods of computer modelling, statistical physics, heat and mass transfer, statistical hydrodynamics, nonlinear dynamics and experimental methods are presented and discussed. Non-equilibrium patterns which appear during macroscopic transport and hydrodynamic flow, chemical reactions, external physical fields (magnetic, electrical, thermal and hydrodynamic) and the impact of external noise on pattern evolution are the foci of this issue. Special attention is paid to pattern formation in biological systems (such as drug transport, hydrodynamic patterns in blood and pattern dynamics in protein and insulin crystals) and to the development of a scientific background for progressive methods of cancer and insult therapy (magnetic hyperthermia for cancer therapy; magnetically induced drug delivery in thrombosed blood vessels). The present issue includes works on pattern growth and their evolution in systems with complex internal structures, including stochastic dynamics, and the influence of internal structures on the external static, dynamic magnetic and mechanical properties of these systems. © 2020 The Author(s) Published by the Royal Society. All rights reserved.Russian Science Foundation, RSF: 18-19-00008Data accessibility. This article has no additional data. Authors’ contributions. All authors contributed equally to the present paper. Competing interests. The authors declare that they have no competing interests. Funding. This work was supported by the Russian Science Foundation (project no. 18-19-00008)