arXiv subjects

P. G. Silvestrov

Publications and source records attributed to P. G. Silvestrov.

At least 37 records · Page 2Linked to original sources

arXiv2007

Spin Effects and Transport in Quantum Dots with overlapping Resonances

The role of spin is investigated in the transport through a quantum dot with two overlapping resonances (one having a width larger than the level separation and the other very narrow, cf. Silvestrov and Imry, Phys. Rev. Lett. {\bf 85}, 2565 (2000)). For a series of consecutive charging resonances, one electron from the leads populates one and the same broad level in the dot. Moreover, there is the tendency to occupy the same level also by the second electron within the same resonance. This second electron is taken from the narrow levels in the dot. The narrow levels are populated (and broad level is depopulated) via sharp rearrangements of the electronic configuration in the Coulomb blockade valleys. Possible experimental manifestations of this scenario are considered. Among these there are sharp features in the valleys and in the Mixed Valence regime and an unusual Kondo effect.

cond-mat.mes-hall↗

arXiv2007

Quantum dots in graphene

We suggest a way of confining quasiparticles by an external potential in a small region of a graphene strip. Transversal electron motion plays a crucial role in this confinement. Properties of thus obtained graphene quantum dots are investigated theoretically for different types of the boundary conditions at the edges of the strip. The (quasi)bound states exist in all systems considered. At the same time, the dependence of the conductance on the gate voltage carries an information about the shape of the edges.

cond-mat.mes-hall↗

arXiv2006

Polarized Electric Current in Semiclassical Transport with Spin-Orbit Interaction

Semiclassical solutions of two-dimensional Schrodinger equation with spin-orbit interaction and smooth potential are considered. In the leading order, spin polarization is in-plane and follows the evolution of the electron momentum for a given subband. Out-of-plane spin polarization appears as a quantum correction, for which an explicit expression is obtained. We demonstrate how spin-polarized currents can be achieved with the help of a barrier or quantum point contact open for transmission only in the lower subband.

cond-mat.mes-hall↗

arXiv2006

Spectrum of the Andreev Billiard and Giant Fluctuations of the Ehrenfest Time

The density of states in the semiclassical Andreev billiard is theoretically studied and shown to be determined by the fluctuations of the classical Lyapunov exponent $λ$. The rare trajectories with a small value of $λ$ give rise to an anomalous increase of the Ehrenfest time $τ_E\approx |\ln\hbar|/λ$ and, consequently, to the appearance of Andreev levels with small excitation energy. The gap in spectrum is obtained and fluctuations of the value of the gap due to different positions of superconducting lead are considered.

cond-mat.mes-hall↗

arXiv2004

On Classical Fluctuations of Ballistic Conductance

Universal conductance fluctuations in disordered systems are one of the most known quantum mesoscopic effects. For ballistic cavity with smooth confining potential however, one should observe a much larger classical sample-to-sample conductance fluctuations. It is shown, how bending of the phase space in case of chaotic dynamics leads to additional enhancement of such fluctuations.

cond-mat.mes-hall↗

arXiv2003

Noiseless scattering states in a chaotic cavity

Shot noise in a chaotic cavity (Lyapunov exponent $λ$, level spacing $δ$, linear dimension $L$), coupled by two $N$-mode point contacts to electron reservoirs, is studied as a measure of the crossover from stochastic quantum transport to deterministic classical transport. The transition proceeds through the formation of {\em fully} transmitted or reflected scattering states, which we construct explicitly. The fully transmitted states contribute to the mean current $\bar{I}$, but not to the shot-noise power $S$. We find that these noiseless transmission channels do not exist for $N\alt\sqrt{k_{F}L}$, where we expect the random-matrix result $S/2e\bar{I}=1/4$. For $N\agt\sqrt{k_{F}L}$ we predict a suppression of the noise $\propto (k_{F}L/N^{2})^{Nδ/π\hbarλ}$. This nonlinear contact dependence of the noise could help to distinguish ballistic chaotic scattering from random impurity scattering in quantum transport.

cond-mat.mes-hall↗

arXiv2003

Adiabatic quantization of Andreev levels

We identify the time $T$ between Andreev reflections as a classical adiabatic invariant in a ballistic chaotic cavity (Lyapunov exponent $λ$), coupled to a superconductor by an $N$-mode point contact. Quantization of the adiabatically invariant torus in phase space gives a discrete set of periods $T_{n}$, which in turn generate a ladder of excited states $ε_{nm}=(m+1/2)π\hbar/T_{n}$. The largest quantized period is the Ehrenfest time $T_{0}=λ^{-1}\ln N$. Projection of the invariant torus onto the coordinate plane shows that the wave functions inside the cavity are squeezed to a transverse dimension $W/\sqrt{N}$, much below the width $W$ of the point contact.

cond-mat.mes-hall↗

arXiv2002

The Enhanced Sensitivity of the Transmission Phase of a Quantum Dot to Kondo Correlations

The strong sensitivity of the transmission phase through a quantum dot embedded into one arm of a two-wave Aharonov-Bohm interferometer to the Kondo effect is explained. The enhancement takes place because of the buildup of the exchange scattering on the dot due to Kondo correlations even much above $T_{K}$. The enhanced exchange competes with the potential scattering, which is always weak. Both cases of the Anderson impurity model and a multilevel quantum dot are considered. In the latter case in addition to the description of peculiar phase behavior a mechanism leading to ferromagnetic Kondo coupling in quantum dots is proposed.

cond-mat.mes-hall↗

arXiv2001

Ehrenfest times for classically chaotic systems

We describe the quantum mechanical spreading of a Gaussian wave packet by means of the semiclassical WKB approximation of Berry and Balazs. We find that the time scale $τ$ on which this approximation breaks down in a chaotic system is larger than the Ehrenfest times considered previously. In one dimension $τ=\fr{7}{6}λ^{-1}\ln(A/\hbar)$, with $λ$ the Lyapunov exponent and $A$ a typical classical action.

nlin.CD↗

arXiv2001

Golden rule decay versus Lyapunov decay of the quantum Loschmidt echo

The overlap of two wave functions evolving in time with slightly different Hamiltonians decays exponentially, for perturbation strengths greater than the level spacing. We present numerical evidence for a dynamical system that the decay rate is given by the smallest of the Lyapunov exponent of the classical chaotic dynamics and the level broadening that follows from the golden rule of quantum mechanics. This limits the range of validity for the perturbation-strength independent decay rate discovered by Jalabert and Pastawski [Phys. Rev. Lett. 86, 2490 (2001)].

nlin.CD↗

arXiv2001

Stretched Exponential Decay of a Quasiparticle in a Quantum Dot

The decay of a quasiparticle in an isolated quantum dot is considered. At relatively small time the probability to find the system in the initial state decays exponentially: $P(t)\sim \exp(-Γt)$, in accordance with the golden rule. However, the contributions to $P(t)$ accounting for the discreteness of final three-particle states, five-particle states, etc. decay much slower being $\sim (Δ_3/Γ)^n \exp(-Γt/(2n+1))$ for $2n+1$ final particles. Here $Δ_3 \ll Γ$ is the level spacing for three-particle states available via the direct decay. These corrections are dominant at large enough time and slow down the decay to become $\ln (P)\sim -\sqrt{t}$ asymptotically. $P(t)$ fluctuates strongly in this regime and the analytical formula for the distribution $W(P)$ is found.

cond-mat.mes-hall↗

arXiv2001

Effect of inelastic scattering on the average Coulomb-blockade peak height in quantum dots

The average height of the Coulomb-blockade conductance peaks for chaotic elastic scattering is known to increase by a factor of 4/3 upon breaking time-reversal symmetry. We calculate the temperature dependence of this factor in the regime that the inelastic scattering rate Gamma_in is greater than the mean tunneling rate Gamma_el, which itself is less than the mean level spacing Delta. Comparison with recent experimental data by Folk et al. (cond-mat/0008052) demonstrates that Gamma_in lies below Gamma_el and hence also below Delta, consistent with the low-energy suppression of inelastic electron-electron scattering in quantum dots.

cond-mat.mes-hall↗

arXiv2000

Limits to error correction in quantum chaos

We study the correction of errors that have accumulated in an entangled state of spins as a result of unknown local variations in the Zeeman energy (B) and spin-spin interaction energy (J). A non-degenerate code with error rate kappa can recover the original state with high fidelity within a time kappa^1/2 / max(B,J) -- independent of the number of encoded qubits. Whether the Hamiltonian is chaotic or not does not affect this time scale, but it does affect the complexity of the error-correcting code.

quant-ph↗

arXiv2000

"Lifshitz tails" and extended states in an Imaginary random potential

Non-Hermitean operators may appear during the calculation of a partition function in various models of statistical mechanics. The tail eigen-states, having anomalously small real part of energy $Re(\eps)$, became naturally important in this case. We consider the distribution of such states and the form of eigenfunctions for the particle propagating in an imaginary random potential (the model motivated by the statistics of polymer chains). Unlike it is in the Hermitean quantum mechanics, our tail states are sufficiently extended. Such state appear if the values of random potential turns out to be anomalously close inside the large area. Results of numerical simulations in the case of strong coupling confirm the analytic estimates.

cond-mat.stat-mech↗

arXiv2000

Towards an Explanation of the Mesoscopic Double-Slit Experiment: a new model for charging of a Quantum Dot

For a quantum dot (QD) in the intermediate regime between integrable and fully chaotic, the widths of single-particle levels naturally differ by orders of magnitude. In particular, the width of one strongly coupled level may be larger than the spacing between other, very narrow, levels. In this case many consecutive Coulomb blockade peaks are due to occupation of the same broad level. Between the peaks the electron jumps from this level to one of the narrow levels and the transmission through the dot at the next resonance essentially repeats that at the previous one. This offers a natural explanation to the recently observed behavior of the transmission phase in an interferometer with a QD.

cond-mat.mes-hall↗

arXiv1999

Scaling at the chaos threshold in an interacting quantum dot

The chaotic mixing by random two-body interactions of many-electron Fock states in a confined geometry is investigated numerically and compared with analytical predictions. Two distinct regimes are found in the dependence of the inverse participation ratio in Fock space I on the dimensionless conductance of the quantum dot g and the excitation energy E. In both regimes I>>1, but only the small-g regime is described by the golden rule. The crossover region is characterized by a maximum in a scaling function that becomes more pronounced with increasing excitation energy. The scaling parameter that governs the transition is (E/g)ln g.

cond-mat.mes-hall↗

arXiv1999

Coulomb blockade in quantum dots with overlapping resonances

Coulomb blockade (CB) in a quantum dot (QD) with one anomalously broad level is considered. In this case many consecutive pronounced CB peaks correspond to occupation of one and the same broad level. Between the peaks the electron jumps from this level to one of the narrow levels and the transmission through the dot at the next resonance essentially repeats that at the previous one. This offers a natural explanation to the recently observed behavior of the transmission phase in an interferometer with a QD. Single particle resonances of very different width are natural if the dot is not fully chaotic. This idea is illustrated by the numerical simulations for a non-integrable QD whose classical dynamics is intermediate between integrable and chaotic. Possible manifestations for the Kondo experiments in the QD are discussed.

cond-mat.mes-hall↗

arXiv1998

Chaos Thresholds in finite Fermi systems

The development of Quantum Chaos in finite interacting Fermi systems is considered. At sufficiently high excitation energy the direct two-particle interaction may mix into an eigen-state the exponentially large number of simple Slater-determinant states. Nevertheless, the transition from Poisson to Wigner-Dyson statistics of energy levels is governed by the effective high order interaction between states very distant in the Fock space. The concrete form of the transition depends on the way one chooses to work out the problem of factorial divergency of the number of Feynman diagrams. In the proposed scheme the change of statistics has a form of narrow phase transition and may happen even below the direct interaction threshold.

cond-mat.mes-hall↗