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A. Alekseev

Publications and source records attributed to A. Alekseev.

At least 19 recordsLinked to original sources
arXiv2025

Non-perturbative macroscopic theory of interfaces with discontinuous dielectric constant

Discontinuity of dielectric constants at the interface is a common feature of all nanostructures and semiconductor heterostructures. Near such interfaces, a charged particle creates a singular self-interaction potential which may be attributed to interaction with fictitious mirror charges. The singularity of this interaction at the interface presents an obstruction to a perturbative approach. In several limiting cases, this problem can be avoided by zeroing out the carrier wave function at the interface. In this paper, we have developed a non-perturbative theory which gives a self-consistent description of carrier propagation through an interface with a dielectric discontinuity. It is based on conservation of the current density propagating through the interface, and it is formulated in terms of general boundary conditions (GBC) for the wave function at the interface with a single phenomenological parameter W. For these GBC, we find exact solutions of the Schrödinger equation near the interface and the carrier energy spectrum including resonances. Using these results, we describe the photo effect at the semiconductor/vacuum interface and the energy spectrum of quantum wells (QWs) at the interface with the vacuum or a high-k dielectric. For a surface of liquid helium, we estimate the parameter W, and match the resulting electron spectrum with the existing experimental data and theoretical analysis.

cond-mat.mtrl-sci↗
arXiv2022

Berezin quantization, conformal welding and the Bott-Virasoro group

Following Nag-Sullivan, we study the representation of the group ${\rm Diff}^+(S^1)$ of diffeomorphisms of the circle on the Hilbert space of holomorphic functions. Conformal welding provides a triangular decompositions for the corresponding symplectic transformations. We apply Berezin formalism and lift this decomposition to operators acting on the Fock space. This lift provides quantization of conformal welding, gives a new representative of the Bott-Virasoso cocylce class, and leads to a surprising identity for the Takhtajan-Teo energy functional on ${\rm Diff}^+(S^1)$.

hep-th↗
arXiv2015

Basics of Low-temperature Refrigeration

This chapter gives an overview of the principles of low temperature refrigeration and the thermodynamics behind it. Basic cryogenic processes - Joule-Thomoson process, Brayton process as well as Claude process - are described and compared. A typical helium laboratory refrigerator based on Claude process is used as a typical example of a low-temperature refrigeration system. A description of the hardware components for helium liquefaction is an important part of this paper, because the design of the main hardware components (compressors, turbines, heat exchangers, pumps, adsorbers, etc.) provides the input for cost calculation, as well as enables to estimate the reliability of the plant and the maintenance expenses. All these numbers are necessary to calculate the economics of a low temperature application.

physics.acc-ph↗
arXiv2010

Observation of a J^PC = 1-+ exotic resonance in diffractive dissociation of 190 GeV/c pi- into pi- pi- pi+

The COMPASS experiment at the CERN SPS has studied the diffractive dissociation of negative pions into the pi- pi- pi+ final state using a 190 GeV/c pion beam hitting a lead target. A partial wave analysis has been performed on a sample of 420000 events taken at values of the squared 4-momentum transfer t' between 0.1 and 1 GeV^2/c^2. The well-known resonances a1(1260), a2(1320), and pi2(1670) are clearly observed. In addition, the data show a significant natural parity exchange production of a resonance with spin-exotic quantum numbers J^PC = 1-+ at 1.66 GeV/c^2 decaying to rho pi. The resonant nature of this wave is evident from the mass-dependent phase differences to the J^PC = 2-+ and 1++ waves. From a mass-dependent fit a resonance mass of 1660 +- 10+0-64 MeV/c^2 and a width of 269+-21+42-64 MeV/c^2 is deduced.

hep-ex↗
arXiv2009

Dirac structures and Dixmier-Douady bundles

A Dirac structure on a vector bundle V is a maximal isotropic subbundle E of the direct sum of V with its dual. We show how to associate to any Dirac structure a Dixmier-Douady bundle A, that is, a Z/2Z-graded bundle of C*-algebras with typical fiber the compact operators on a Hilbert space. The construction has good functorial properties, relative to Morita morphisms of Dixmier-Douady bundles. As applications, we show that the `spin' Dixmier-Douady bundle over a compact, connected Lie group (as constructed by Atiyah-Segal) is multiplicative, and we obtain a canonical `twisted Spin-c-structure' on spaces with group valued moment maps.

math.DG↗
arXiv2009

Kontsevich deformation quantization and flat connections

In arXiv:math/0105152, the second author used the Kontsevich deformation quantization technique to define a natural connection ω_n on the compactified configuration spaces of n points on the upper half-plane. This connection takes values in the Lie algebra of derivations of the free Lie algebra with n generators. In this paper, we show that ω_n is flat. The configuration space contains a boundary stratum at infinity which coincides with the (compactified) configuration space of n points on the complex plane. When restricted to this stratum, ω_n gives rise to a flat connection ω_n^\infty. We show that the parallel transport Φdefined by ω_3^\infty between configuration 1(23) and (12)3 verifies axioms of an associator. We conjecture that ω_n^\infty takes values in the Lie algebra of infinitesimal braids. This conjecture implies that Φis an even Drinfeld associator defining a new explicit solution of associator axioms. A proof of this conjecture has recently appeared in arXiv:0905.1789

math.QA↗
arXiv2009

Drinfeld associators, braid groups and explicit solutions of the Kashiwara-Vergne equations

The Kashiwara-Vergne (KV) conjecture states the existence of solutions of a pair of equations related with the Campbell-Baker-Hausdorff series. It was solved by Meinrenken and the first author over the real numbers, and in a formal version, by the first and last authors over a field of characteristic 0. In this paper, we give a simple and explicit formula for a map from the set of Drinfeld associators to the set of solutions of the formal KV equations. Both sets are torsors under the actions of prounipotent groups, and we show that this map is a morphism of torsors. When specialized to the KZ associator, our construction yields a solution over the reals of the original KV conjecture.

math.QA↗
arXiv2008

The Atiyah algebroid of the path fibration over a Lie group

Let G be a connected Lie group, LG its loop group, and PG->G the principal LG-bundle defined by quasi-periodic paths in G. This paper is devoted to differential geometry of the Atiyah algebroid A=T(PG)/LG of this bundle. Given a symmetric bilinear form on the Lie algebra g and the corresponding central extension of Lg, we consider the lifting problem for A, and show how the cohomology class of the Cartan 3-form on G arises as an obstruction. This involves the construction of a 2-form on PG with differential the pull-back of the Cartan form. In the second part of this paper we obtain similar LG-invariant primitives for the higher degree analogues of the Cartan form, and for their G-equivariant extensions.

math.DG↗
arXiv2005

On the Kashiwara-Vergne conjecture

Let $G$ be a connected Lie group, with Lie algebra $g$. In 1977, Duflo constructed a homomorphism of $g$-modules $Duf: S(g) -> U(g)$, which restricts to an algebra isomorphism on invariants. Kashiwara and Vergne (1978) proposed a conjecture on the Campbell-Hausdorff series, which (among other things) extends the Duflo theorem to germs of bi-invariant distributions on the Lie group $G$. The main results of the present paper are as follows. (1) Using a recent result of Torossian (2002), we establish the Kashiwara-Vergne conjecture for any Lie group $G$. (2) We give a reformulation of the Kashiwara-Vergne property in terms of Lie algebra cohomology. As a direct corollary, one obtains the algebra isomorphism $H(g,S(g)) -> H(g,U(g))$, as well as a more general statement for distributions.

math.QA↗
arXiv2005

Ginzburg-Weinstein via Gelfand-Zeitlin

Let U(n) be the unitary group, and $u(n)^*$ the dual of its Lie algebra, equipped with the Kirillov Poisson structure. In their 1983 paper, Guillemin-Sternberg introduced a densely defined Hamiltonian action of a torus of dimension $(n-1)n/2$ on $u(n)^*$, with moment map given by the Gelfand-Zeitlin coordinates. A few years later, Flaschka-Ratiu described a similar, `multiplicative' Gelfand-Zeitlin system for the Poisson Lie group $U(n)^*$. By the Ginzburg-Weinstein theorem, $U(n)^*$ is isomorphic to $u(n)^*$ as a Poisson manifold. Flaschka-Ratiu conjectured that one can choose the Ginzburg-Weinstein diffeomorphism in such a way that it intertwines the linear and nonlinear Gelfand-Zeitlin systems. Our main result gives a proof of this conjecture, and produces a canonical Ginzburg-Weinstein diffeomorphism.

math.DG↗
arXiv2005

Equivariant cohomology and the Maurer-Cartan equation

Let G be a compact, connected Lie group, acting smoothly on a manifold M. Goresky-Kottwitz-MacPherson described a small Cartan model for the equivariant cohomology of M, quasi-isomorphic to the standard Cartan complex of equivariant differential forms. In this paper, we construct an explicit cochain map from the small Cartan model into the standard Cartan model, inducing an isomorphism in cohomology. The construction involves the solution of a remarkable inhomogeneous Maurer-Cartan equation. This solution has further applications to the theory of transgression in the Weil algebra, and to the Chevalley-Koszul theory of the cohomology of principal bundles.

math.DG↗
arXiv2003

Lie theory and the Chern-Weil homomorphism

We introduce a canonical Chern-Weil map for possibly non-commutative g-differential algebras with connection. Our main observation is that the generalized Chern-Weil map is an algebra homomorphism ``up to g-homotopy''. Hence, the induced map from invariant polynomials to the basic cohomology is an algebra homomorphism. As in the standard Chern-Weil theory, this map is independent of the choice of connection. Applications of our results include: a conceptually easy proof of the Duflo theorem for quadratic Lie algebras, a short proof of a conjecture of Vogan on Dirac cohomology, generalized Harish-Chandra projections for quadratic Lie algebras, an extension of Rouviere's theorem for symmetric pairs, and a new construction of universal characteristic forms in the Bott-Shulman complex.

math.RT↗
arXiv2002

Clifford algebras and the classical dynamical Yang-Baxter equation

We describe a relationship of the classical dynamical Yang-Baxter equation with the following elementary problem for Clifford algebras: Given a vector space $V$ with quadratic form $Q_V$, how is the exponential of an element in $\wedge^2(V)$ under exterior algebra multiplication related to its exponential under Clifford multiplication?

math.RT↗
arXiv2002

Optimal quantum pumps have a vanishing transmission coefficient

In a recent Letter, Avron et. al (math-ph/0105011) introduced a notion of optimal quantum pumps. These are adiabatic quantum pumps which work without dissipation. In particular, they produce neither entropy nor noise. In the present Comment we show that in the absence of magnetic field optimal quantum pumps always have a vanishing transmission coefficient. Such `quantum pumps' do not make use of Quantum Mechanics since all tunneling or interference effects are banned by vanishing of the transmission coefficient. We leave it as an outstanding question whether genuine optimal quantum pumps with nonvanishing transmission coefficient can be constructed by making use of the magnetic field.

cond-mat.mes-hall↗
arXiv2000

On B-independence of RR charges

Generalization of the recent Taylor-Polchinski argument is presented, which helps to explain quantization of RR charges in IIA-like theories in the presence of cohomologically trivial H-fields.

hep-th↗