arXiv subjects

S. A. Gurvitz

Publications and source records attributed to S. A. Gurvitz.

At least 37 records · Page 2Linked to original sources

arXiv2002

Two-electron correlated motion due to Coulomb repulsion

A Hubbard-type model is derived from the microscopic Schrödinger equation. We found that additional terms describing direct two-electron transitions must be added to the standard Hubbard Hamiltonian. Such a Hamiltonian generates two-electron pairing due to on-site Coulomb repulsion. We demonstrate that the electron pairs with opposite spin propagate across periodic structures via direct and sequential two-electron tunneling. This mechanism can be used for a generation of entangled electron current. Numerical calculations show stability of the electron pairs.

cond-mat↗

arXiv2002

Two-potential approach to multi-dimensional tunneling

We consider tunneling to the continuum in a multi-dimensional potential. It is demonstrate that this problem can be treated as two separate problems: a) a bound state and b) a non-resonance scattering problem, by a proper splitting of the potential into two components. Finally we obtain the resonance energy and the partial tunneling widths in terms of the bound and the scattering state wave functions. This result can be used in a variety of tunneling problems. As an application we consider the ionization of atomic states by an external field. We obtain very simple analytical expressions for the tunneling width and for the angular distribution of tunneling electrons. It is shown that the angular spread of electrons in the final state is determined by the semi-classical traversal tunneling time.

nucl-th↗

arXiv2001

Shot noise in coupled dots and the "fractional charges"

We consider the problem of shot noise in resonant tunneling through double quantum dots in the case of interacting particles. Using a many-body quantum mechanical description we evaluate the energy dependent transmission probability, the total average current and the shot noise spectrum. Our results show that the obtained reduction of the noise spectrum, due to Coulomb interaction, can be interpret in terms of non--interacting particles with fractional charge like behavior.

cond-mat↗

arXiv2001

Relativistic approaches to structure functions of nuclei

We employ a propagator technique to derive a new relativistic $1/\qq$ expansion of the structure function of a nucleus, composed of point-nucleons. We exploit non-relativistic features of low-momentum nucleons in the target and only treat relativistically the nucleon after absorption of a high-momentum virtual photon. The new series permits a 3-dimensional reduction of each term and a formal summation of all Final State Interaction terms. We then show that a relativistic structure function can be obtained from its non-relativistic analog by a mere change of a scaling variable and an addition of an energy shift. We compare the obtained result with an ad hoc generalized Gersch-Rodriguez-Smith theory, previously used in computations of nuclear structure functions.

nucl-th↗

arXiv2001

Quantum Measurement of a Single Spin using Magnetic Resonance Force Microscopy

Single-spin detection is one of the important challenges facing the development of several new technologies, e.g. single-spin transistors and solid-state quantum computation. Magnetic resonance force microscopy with a cyclic adiabatic inversion, which utilizes a cantilever oscillations driven by a single spin, is a promising technique to solve this problem. We have studied the quantum dynamics of a single spin interacting with a quasiclassical cantilever. It was found that in a similar fashion to the Stern-Gerlach interferometer the quantum dynamics generates a quantum superposition of two quasiclassical trajectories of the cantilever which are related to the two spin projections on the direction of the effective magnetic field in the rotating reference frame. Our results show that quantum jumps will not prevent a single-spin measurement if the coupling between the cantilever vibrations and the spin is small in comparison with the amplitude of the radio-frequency external field.

quant-ph↗

arXiv2001

Formation and Dynamics of a Schrödinger-Cat State in Continuous Quantum Measurement

We consider the process of a single-spin measurement using magnetic resonance force microscopy (MRFM) as an example of a truly continuous measurement in quantum mechanics. This technique is also important for different applications, including a measurement of a qubit state in quantum computation. The measurement takes place through the interaction of a single spin with a quasi-classical cantilever, modeled by a quantum oscillator in a coherent state in a quasi-classical region of parameters. The entire system is treated rigorously within the framework of the Schrödinger equation, without any artificial assumptions. Computer simulations of the spin-cantilever dynamics, where the spin is continuously rotated by means of cyclic adiabatic inversion, show that the cantilever evolves into a Schrödinger-cat state: the probability distribution for the cantilever position develops two asymmetric peaks that quasi-periodically appear and vanish. For a many-spin system our equations reduce to the classical equations of motion, and we accurately describe conventional MRFM experiments involving cyclic adiabatic inversion of the spin system. We surmise that the interaction of the cantilever with the environment would lead to a collapse of the wave function; however, we show that in such a case the spin does not jump into a spin eigenstate.

quant-ph↗

arXiv2000

Delocalization in the Anderson model due to a local measurement

We study a one-dimensional Anderson model in which one site interacts with a detector monitoring the occupation of that site. We demonstrate that such an interaction, no matter how weak, leads to total delocalization of the Anderson model, and we discuss the experimental consequences

cond-mat↗

arXiv2000

Influence of measurement on the life-time and the line-width of unstable systems

We investigate the quantum Zeno effect in the case of electron tunneling out of a quantum dot in the presence of continuous monitoring by a detector. It is shown that the Schrödinger equation for the whole system can be reduced to Bloch-type rate equations describing the combined time-development of the detector and the measured system. Using these equations we find that continuous measurement of the unstable system does not affect its exponential decay to a reservoir with a constant density of states. The width of the energy distribution of the tunneling electron, however, is not equal to the inverse life-time -- it increases due to the decoherence generated by the detector. We extend the analysis to the case of a reservoir described by an energy dependent density of states, and we show that continuous measurement of such quantum systems affects both the exponential decay rate and the energy distribution. The decay does not always slow down, but might be accelerated. The energy distribution of the tunneling electron may reveal the lines invisible before the measurement.

quant-ph↗

arXiv2000

Effect of the measurement on the decay rate of a quantum system

We investigated the electron tunneling out of a quantum dot in the presence of a continuous monitoring by a detector. It is shown that the Schrödinger equation for the whole system can be reduced to new Bloch-type rate equations describing the time-development of the detector and the measured system at once. Using these equations we find that the continuous measurement of the unstable system does not affect its exponential decay, $\exp (-Γt)$, contrary to expectations based on the Quantum Zeno effect . However, the width of the energy distribution of the tunneling electron is no more $Γ$, but increases due to the decoherence, generated by the detector.

quant-ph↗

arXiv1999

Dephasing and collapse in continuous measurement of a single system

We show that long standing debates on the collapse and the role of the observer in quantum mechanics can be resolved experimentally via a nondistructive continuous monitoring of a single quantum system. An example of such a system, coupled with the point-contact detector is presented. The detailed quantum mechanical analysis of the entire system (including the detector) shows that under certain conditions the measurement collapse would generate distinctive effects in the detector behavior, which can be experimentally investigated.

quant-ph↗

arXiv1998

Density-matrix approach to coherent transport and the measurement problem

Bloch-type equations for description of coherent transport in mesoscopic systems are applied for a study of the continuous measurement process. Both the detector and the measured system are described quantum mechanically. It is shown that the Schrödinger evolution of the entire system cannot be accommodated with the measurement collapse. The latter leads to quantum jumps which can be experimentally detected.

quant-ph↗

arXiv1997

Rate equations for quantum transport in multi-dot systems

Starting with the many-body Schrödinger equation we derive new rate equations for resonant transport in quantum dots linked by ballistic channels with high density of states. The charging and the Pauli exclusion principle effects were taken into account. It is shown that the current in such a system displays quantum coherence effects, even if the dots are away one from another. A comparative analysis of quantum coherence effects in coupled and separated dots is presented. The rate equations are extended for description of coherent and incoherent transport in arbitrary multi-dot systems. It is demonstrated that new rate equations constitute a generalization of the well-known optical Bloch equations.

cond-mat.mes-hall↗

arXiv1997

Measurements with a noninvasive detector and dephasing mechanism

We study dynamics of the measurement process in quantum dot systems, where a particular state out of coherent superposition is observed. The ballistic point-contact placed near one of the dots is taken as a noninvasive detector. We demonstrate that the measurement process is fully described by the Bloch-type equations applied to the whole system. These equations clearly reproduce the collapse of the density-matrix into the statistical mixture in the course of the measurement process. The corresponding dephasing width is uniquely defined. We show that the continuous observation of one of the states in a coherent superposition may accelerate decay from this state -- in contradiction with rapidly repeated observations, which slow down the transitions between quantum states (the quantum Zeno effect).

cond-mat.mes-hall↗

arXiv1997

Confinement and scaling in deep inelastic processes

We show that parton confinement in the final state generates large $1/Q^2$ (higher twist) corrections to Bjorken scaling. For treatment of these non-perturbative effects, we derive a new expansion in powers of $1/Q^2$ for the structure function that is free of infra-red singularities and which reduces corrections to the leading term. The leading term represents scattering from an off-mass-shell parton, which keeps the same virtual mass in the final state. This term appears as a function of a new variable $\bar x(x,Q^2)$, which coincides with the Bjorken variable x for $Q^2\to\infty$. Analysis of the data shows excellent scaling at large x, where power corrections are dominant. The approach accommodates also the QCD logarithmic corrections and the behavior of the structure functions is well reproduced within a wide kinematical range. Since the new scaling variable $\bar x(x,Q^2)$ incorporates the higher twist effects, it allows us to extract the ratio $F_2^n(x)/F_2^p(x)$ for $x\to 1$ from the available data at moderate Q^2.

nucl-th↗

arXiv1996

Interaction-Free Measurement in mesoscopic systems and the reduction postulate

We show that a noninvasive,``negative-result measurement'' can be realized in quantum dot systems. The measurement process is studied by applying the Schrödinger equation to the whole system (including the detector). We demonstrate that the possibility of observing a particular state out of coherent superposition leads to collapse of the corresponding nondiagonal density-matrix elements of the measured system. No additional reduction postulate is needed. Experimental consequences of the collapse time and the relativistic requirement are discussed for mesoscopic and optical systems.

quant-ph↗

arXiv1996

Scaling approach to higher-twist corrections

Bjorken scaling is violetd. At large $x$-values ($0.7 \lesssim x \leq 1$) the violation is mainly attributed to $\propto 1/Q^2$ (higher-twist) corrections. We discuss how to incorporate such corrections by using a new scaling variable $\bar x(x,Q^2)$ which accounts for the non-perturbative effects due to the confining parton interaction in the final state. The approach can accomodate also the remaining QCD logarithmic corrections and the behaviour of the $F_2(x,Q^2)$ structure functions is reproduced, in a quite natural way, within a wide kinematical range.

hep-ph↗

arXiv1996

Quantum transport in mesoscopic systems and the measurement problem

We study noninvasive measurement of stationary currents in mesoscopic systems. It is shown that the measurement process is fully described by the Schrödinger equation without any additional reduction postulate and without the introduction of an observer. Nevertheless the possibility of observing a particular state out of coherent superposition leads to collapse of the wave function, even though the measured system is not distorted by interaction with the detector. Experimental consequences are discussed.

quant-ph↗

arXiv1996

Microscopic derivation of rate equations for quantum transport

It is shown that under certain conditions the resonant transport in mesoscopic systems can be described by modified (quantum) rate equations, which resemble the optical Bloch equations with some additional terms. Detailed microscopic derivation from the many-body Schrödinger equation is presented. Special attention is paid to the Coulomb blockade and quantum coherence effects in coupled quantum dot systems. The distinction between classical and quantum descriptions of resonant transport is clearly manifested in the modified rate equations.

cond-mat↗