arXiv subjects

Gleb A. Skorobagatko

Publications and source records attributed to Gleb A. Skorobagatko.

7 recordsLinked to original sources

arXiv2021

Restrictions on the existence of weak values in quantum mechanics: weak quantum evolution concept

It is shown, that the Aharonov-Albert-Vaidman concept of weak values appears to be a consequence of a more general quantum phenomenon of weak quantum evolution. Here the concept of weak quantum evolution is introduced and discussed for the first time. In particular, it is shown on the level of quantum evolution that there exist restrictions on the applicability of weak quantum evolution- and, hence, weak values approach. These restrictions connect the size of given quantum ensemble with the parameters of pre- and post-selected quantum states. It is shown, that the latter requirement can be fulfilled for the model system, where the concept of weak values was initially introduced by Aharonov,Vaidman and Albert. Moreover, a deep connection between weak quantum evolution and conventional probability of quantum transition between two non-orthogonal quantum states is established for the first time. It is found that weak quantum evolution of quantum system between its two non-orthogonal quantum states is inherently present in the measurement-determined definition of quantum transition probability between these two quantum states.

quant-ph↗

arXiv2021

Universal separability criterion for arbitrary density matrices from causal properties of separable and entangled quantum states

General physical background of Peres-Horodecki positive partial transpose (ppt-) separability criterion is revealed. Especially, the physical sense of partial transpose operation is shown to be equivalent to the "local causality reversal" (LCR-) procedure for all separable quantum systems or to the uncertainty in a global time arrow direction in all entangled cases. Using these universal causal considerations the heuristic causal separability criterion has been proposed for arbitrary $ D^{N} \times D^{N}$ density matrices acting in $ \mathcal{H}_{D}^{\otimes N} $ Hilbert spaces which describe the ensembles of $ N $ quantum systems of $ D $ eigenstates each. Resulting general formulas have been then analyzed for the widest special type of one-parametric density matrices of arbitrary dimensionality, which model equivalent quantum subsystems being equally connected (EC-) with each other by means of a single entnaglement parameter $ p $. In particular, for the family of such EC-density matrices it has been found that there exists a number of $ N $- and $ D $-dependent separability (or entanglement) thresholds $ p_{th}(N,D) $ which in the case of a qubit-pair density matrix in $ \mathcal{H}_{2} \otimes \mathcal{H}_{2} $ Hilbert space are shown to reduce to well-known results obtained earlier by Peres [5] and Horodecki [6]. As the result, a number of remarkable features of the entanglement thresholds for EC-density matrices has been described for the first time. All novel results being obtained for the family of arbitrary EC-density matrices are shown to be applicable for a wide range of both interacting and non-interacting multi-partite quantum systems, such as arrays of qubits, spin chains, ensembles of quantum oscillators, strongly correlated quantum many-body systems with the possibility of many-body localization, etc.

quant-ph↗

arXiv2020

Self-equilibration theorem in quantum-point contacts of interacting electrons: time-dependent quantum fluctuations of tunnel transport beyond the Levitov-Lesovik scattering approach

Equilibration to the steady state for a wide class of Luttinger liquid ballistic weakly linked tunnel contacts is extensively studied. Quantum fluctuations of tunnel current are considered in all orders in tunnel coupling and out of the equilibrium in the time domain. Especially, two important mathematical statements: Self-equilibration (SE-)theorem and Self-equilibration (SE-)lemma on the exact re-exponentiation of thermal average from the Keldysh-contour-ordered evolution operator for arbitrary weakly linked Luttinger liquid tunnel contact are proven. Demonstrated proof of SE-theorem and SE-lemma represents first evidence of a novel emergent phenomenon of "self-equilibration" in the dynamics of quantum fluctuations of electron transport through ballistic tunnel junctions. This phenomenon and all related real-time full counting statistics are shown to be much more general as compared to the usual Levitov-Lesovik scattering approach for the non-interacting electrons, though SE-theorem also contains known results obtained within the Levitov-Lesovik scattering approach as corresponding limiting case for lowest order cumulants at $ g=1 $. As the result, corresponding differential equation of "self-equilibration" for time-dependent Keldysh partition function of tunnel contact is derived and explained. As the consequence of obtained results, a universal character of self-equilibration of tunnel current in one-dimensional weakly linked tunnel junctions is revealed and studied on the level of non-equilibrium Fano factor. As well, a new measure of disequilibrium in such systems - the "steady flow" rate - is also introduced and discussed.

cond-mat.str-el↗

arXiv2018

Theory of interaction-dependent instability in quantum detection by means of Luttinger liquid tunnel junction: a rigorous theorem

The low-temperature regime of charge-qubit decoherence due to its Coulomb interaction with electrons tunneling through Luttinger liquid quantum-point contact (QPC) is investigated. The study is focused on quantum detector properties of Luttinger liquid QPC. It is shown, that in low-temperature limit the respective perturbative decoherence- and acquisition of information timescales both tend to diverge, thus, shadowing a true picture of low-temperature quantum detection for such quantum systems. Here I prove two general mathematical statements (S-theorem and S-lemma) about exact re-exponentiation of Keldysh-contour ordered T-exponent for arbitrary Luttinger liquid tunnel Hamiltonian. As the result, decoherence- and acquisition of information time-scales as well as QPC quantum detector efficiency rate are calculated exactly and are shown to have a dramatic dependence on repulsive interaction between electrons in 1D leads of QPC. Discovered abrupt decrease of QPC quantum detector efficiency $ Q $ with the increase of $ g $ in the close vicinity of value $ g_{cr}(T) $ represents a fingerprint of interaction-dependent instability of all the quantum detection procedure for any Luttinger liquid QPC quantum detector at definite low enough temperatures $ T_{cr}(g) $. The reasons behind these effects are discussed. Also, it is shown that such the low-temperature detection instability effect is able to explain a large unclear mismatch between expected and observed decoherence timescales in two well-known experiments (J.Gorman, D.G.Hasko, D.A.Williams, Phys.Rev.Lett., 95, 090502 (2005); K.D.Petersson, J.R.Petta, H.Lu, A.C.Gossard, Phys.Rev.Lett., 105, 246804 (2010);) on charge-qubit quantum dynamics.

cond-mat.str-el↗

arXiv2013

Aharonov-Bohm phase-driven resonant tunneling of interacting electrons in magnetopolaronic Majorana-Resonant-Level Model

The magnetopolaronic generalization of a Majorana-resonant-level (-MRL) model is considered for a single-level vibrating quantum dot symmetrically coupled to two half-infinite $g=1/2$- Tomonaga-Luttinger liquid (-TLL) leads at the Toulouse point. At the resonance by gate voltage the exact solution for the effective transmission coefficient is obtained in the whole range of magnetopolaronic coupling constant values. The obtained exact solution exists due to special Majorana-like symmetry of tunnel Hamiltonian and gives rise to nontrivial interference between different virtual vibronic channels of resonant tunneling with different fixed Aharonov-Bohm phases. This fact leads to a novel topologically nontrivial type of resonant Andreev-like magnetopolaronic tunneling in the system. As the result, in the zero-temperature limit, it is impossible to compensate the magnetopolaronic blockade in magnetopolaronic MRL-model by means of bias voltage, if vibron energy is the smallest (but nonzero) energy parameter in the system.

cond-mat.str-el↗

arXiv2013

Polaronic effects in electron shuttling

Shuttle-like mechanism of electron transport through a single level vibrating quantum dot is considered in the regime of strong electromechanical coupling. It is shown that the increment of shuttle instability is a nonmonotonic function of the driving voltage. The interplay of two oppositely acting effects - vibron-assisted electron tunneling and polaronic blockade - results in oscillations of the increment on the energy scale of vibron energy.

cond-mat.mes-hall↗

arXiv2012

Resonant polaron-assisted tunneling of strongly interacting electrons through a single-level vibrating quantum dot

The problem of resonant transport of strongly interacting electrons through a one-dimensional single-level vibrating quantum dot is being considered. In this paper, we generalize the Komnik and Gogolin model [Phys. Rev. Lett., 90, 246403, (2003)] for the single-electron transistor with g=1/2 Luttinger liquid leads to the case of a strong electron-vibron interaction in a quantum dot. The effective transmission coefficient and differential conductance of the system has been derived for the general case of asymmetric tunnel barriers. The main result obtained is that, in the zero-temperature limit, the resonant polaron-assisted tunneling with perfect transmission is possible. This resonant tunneling is of the novel (Andreev-like) type due to a special electron-electron interaction in the leads. As a result, a strong domination of resonant polaron-assisted electron transport at low temperatures has been found. Additional narrowing due to electron-electron interaction in the leads, is roughly the same for all polaron-assisted resonances.

cond-mat.str-el↗