arXiv subjects
Publications and source records attributed to A. V. Lebedev.
We present a non-perturbative expression for the scattering matrix of $N$ particles interacting inside a quantum dot. Characterizing the dot by its resonances, we find a compact form for the scattering matrix in a real-time representation. We study the transmission probabilities and interaction-induced orbital entanglement of two electrons incident on the dot in a spin-singlet state.
The dynamics of a particle interacting with random classical field in a two-well potential is studied by the functional integration method. The probability of particle localization in either of the wells is studied in detail. Certain field-averaged correlation functions for quantum-mechanical probabilities and the distribution function for the probabilities of final states (which can be considered as random variables in the presence of a random field) are calculated. The calculated correlators are used to discuss the dependence of the final state on the initial state. One of the main results of this work is that, although the off-diagonal elements of density matrix disappear with time, a particle in the system is localized incompletely (wave-packet reduction does not occur), and the distribution function for the probability of finding particle in one of the wells is a constant at infinite time.
Adopting the frame of mesoscopic physics, we describe a Bell type experiment involving time-delayed two-particle correlation measurements. The indistinguishability of quantum particles results in a specific interference between different trajectories. We show how the non-locality in the time-delayed correlations due to the indistinguishability of the quantum particles manifests itself in the violation of a Bell inequality, where the degree of violation is related to the accuracy of the measurement. We demonstrate how the interrelation between the orbital- and the spin exchange symmetry can by exploited to infer knowledge on spin-entanglement from a measurement of orbital entanglement.
The article discusses the interrelation between relative Cuntz-Pimsner algebras and partial isometric crossed products, and presents a procedure that reduces any given Hilbert bimodule to the "smallest" Hilbert bimodule yielding the same relative Cuntz-Pimsner algebra as the initial one. In the context of crossed products this reduction procedure corresponds to reduction of C*-dynamical systems.
Starting from an arbitrary endomorphism δof a unital C*-algebra A we construct a crossed product. It is shown that the natural construction depends not only on the C*-dynamical system (A,δ) but also on the choice of an ideal J orthogonal to Ker δ.
Certain inequalities between the values of the modular and the norm in the Orlicz spaces are established. These inequalities are applied then to the theory of solvability of nonlinear integral equations of Hammerstein type.
We suggest an operating scheme for the deliberate generation of spin-entangled electron pairs in a normal-metal mesoscopic structure with fork geometry. Voltage pulses with associated Faraday flux equal to one flux unit $Φ_0=hc/e$ drive individual singlet-pairs of electrons towards the beam splitter. The spin-entangled pair is created through a post-selection in the two branches of the fork. We analyze the appearance of entanglement in a Bell inequality test formulated in terms of the number of transmitted electrons with a given spin polarization.
The paper presents a construction of the crossed product of a C*-algebra by a semigroup of endomorphisms generated by partial isometries.
We propose a novel method for detecting gravitational waves (GW), where a light signal emitted from a distant star interacts with a local (also distant) GW source and travels towards the Earth, where it is detected. While traveling in the field of the GW, the light acquires specific phase modulation (which we account in the eikonal approximation). This phase modulation can be considered as a coherent spreading of the given initial photons energy over a set of satellite lines, spaced at the frequency of GW (from quantum point of view it is multi-graviton absorption and emission processes). This coherent state of photons with the energy distributed among the set of equidistant lines, can be analyzed and identified on Earth either by passing the signal through a Fabry-Perot filter or by monitoring the intensity-intensity correlations at different times.
The paper presents a criterion for a C*-algebra to be a coefficient algebra associated with a given endomorphism
The paper presents a construction of the crossed product of a C*-algebra by an endomorphism generated by partial isometry
We determine the non-local in time and space current-current cross correlator $<\hat{I}(x_1,t_1) \hat{I}(x_2,t_2)>$ in a mesoscopic conductor with a scattering center at the origin. Its excess part appearing at finite voltage exhibits a unique dependence on the retarded variable $t_1-t_2-(|x_1|-|x_2|)/ v_{\rm\scriptscriptstyle F}$, with $v_{\rm\scriptscriptstyle F}$ the Fermi velocity. The non-monotonic dependence of the retardation on $x_1$ and its absence at the symmetric position $x_1 = -x_2$ is a signature of the wave function collapse, which thus becomes amenable to observation in a mesoscopic solid state device.
We study the time dependent electron-electron and electron-hole correlations in a mesoscopic device which is splitting an incident current of free fermions into two spatially separated particle streams. We analyze the appearance of entanglement as manifested in a Bell inequality test and discuss its origin in terms of local spin-singlet correlations already present in the initial channel and the action of post-selection during the Bell type measurement. The time window over which the Bell inequality is violated is determined in the tunneling limit and for the general situation with arbitrary transparencies. We compare our results with alternative Bell inequality tests based on coincidence probabilities.
The article presents the procedure of the index calculation for the elements of the algebra generated by one dimensional singular integral operators with discontinuous oscillating coefficients.
We present a theoretical analysis of the appearance of entanglement in non-interacting mesoscopic structures. Our setup involves two oppositely polarized sources injecting electrons of opposite spin into the two incoming leads. The mixing of these polarized streams in an ideal four-channel beam splitter produces two outgoing streams with particular tunable correlations. A Bell inequality test involving cross-correlated spin-currents in opposite leads signals the presence of spin-entanglement between particles propagating in different leads. We identify the role of fermionic statistics and projective measurement in the generation of these spin-entangled electrons.
The basic notion of the article is a pair (A,U), where A is a commutative C*-algebra and U is a partial isometry such that mapping U()U* is an endomorphism of A and U*U belongs to A. We give a description of the maximal ideal space of the smallest coefficient C*-algebra of the algebra C*(A,U) generated by the system (A,U).
Although quantum mechanics is a mature theory, fundamental problems discussed during its time of foundation have remained with us to this day. These problems are centered on the problematic relation between the quantum and classical worlds. The most famous element is the measurement problem, i.e., the measurement of a quantum system by a classical apparatus, and the concomitant phenomena of wave packet reduction, the appearance of probability, and the problems related to Schrödinger cat states. A fundamental question in this context is whether quantum mechanics can bootstrap itself to the classical world: is quantum mechanics self-consistent, such that the measurement process can be understood within quantum mechanics itself, or does this process require additional elements from the realm outside of traditional quantum mechanics? Here, we point to a problematic aspect in the traditional Schrödinger cat argument which can be overcome through its extension with a proper macroscopic preparation device; the deliberate creation of a cat state and its identification then turns into a non-trivial problem requiring the determination of the evolution of a quantum system entangled with a macroscopic reservoir. We describe a new type of wave-function correlator testing for the appearance of Schrödinger cat states and discuss its implications for theories deriving the wave function collapse from a unitary evolution.
In this paper we investigate the interrelation between the topological freedom of partial actions of discrete groups and faithful representations of partial crossed products.