arXiv subjects

V. Cheianov

Publications and source records attributed to V. Cheianov.

17 recordsLinked to original sources

arXiv2025

Exact S-matrices for higher dimensional representations of generalized Landau-Zener Hamiltonians

We explore integrable Landau-Zener-type Hamiltonians through the framework of Lie algebraic structures. By reformulating the classic two-level Landau-Zener model as a Lax equation, we show that higher-spin generalizations lead to exactly solvable scattering matrices, which can be computed efficiently for any higher-spin representation. We further extend this approach to generalized bow-tie Landau-Zener Hamiltonians, employing non-Abelian gauge fields that satisfy a zero-curvature condition to derive their scattering matrices algebraically. This method enables the systematic construction of new exactly solvable multi-level models; as a result, we present previously unknown six-dimensional and eight-dimensional Landau-Zener models.

quant-ph↗

arXiv2024

Integrability and chaos in the quantum brachistochrone problem

The quantum brachistochrone problem addresses the fundamental challenge of achieving the quantum speed limit in applications aiming to realize a given unitary operation in a quantum system. Specifically, it looks into optimization of the transformation of quantum states through controlled Hamiltonians, which form a small subset in the space of the system's observables. Here we introduce a broad family of completely integrable brachistochrone protocols, which arise from a judicious choice of the control Hamiltonian subset. Furthermore, we demonstrate how the inherent stability of the completely integrable protocols makes them numerically tractable and therefore practicable as opposed to their non-integrable counterparts.

quant-ph↗

arXiv2022

Heisenberg's uncertainty principle in the PTOLEMY project: a theory update

We discuss the consequences of the quantum uncertainty on the spectrum of the electron emitted by the $β$-processes of a tritium atom bound to a graphene sheet. We analyze quantitatively the issue recently raised in [Cheipesh et al., Phys. Rev. D 104, 116004 (2021)], and discuss the relevant time scales and the degrees of freedom that can contribute to the intrinsic spread in the electron energy. We perform careful calculations of the potential between tritium and graphene with different coverages and geometries. With this at hand, we propose possible avenues to mitigate the effect of the quantum uncertainty.

hep-ph↗

arXiv2022

An ideal rapid-cycle Thouless pump

Thouless pumping is a fundamental instance of quantized transport, which is topologically protected. Although its theoretical importance, the adiabaticity condition is an obstacle for further practical applications. Here, focusing on the Rice-Mele model, we provide a family of finite-frequency examples that ensure both the absence of excitations and the perfect quantization of the pumped charge at the end of each cycle. This family, which contains an adiabatic protocol as a limiting case, is obtained through a mapping onto the zero curvature representation of the Euclidean sinh-Gordon equation.

cond-mat.mes-hall↗

arXiv2021

Rapid-cycle Thouless pumping in a one-dimensional optical lattice

An adiabatic cycle around a degeneracy point in the parameter space of a one-dimensional band insulator is known to result in an integer valued noiseless particle transport in the thermodynamic limit. Recently, it was shown that in the case of an infinite bipartite lattice the adiabatic Thouless protocol can be continuously deformed into a fine tuned finite-frequency cycle preserving the properties of noiseless quantized transport. In this paper, we numerically investigate the implementation of such an ideal rapid-cycle Thouless pumping protocol in a one-dimensional optical lattice. It is shown that the rapidity will cause first order corrections due to next-to-nearest-neighbour hopping and second order corrections due to the addition of a harmonic potential. Lastly, the quantization of the change in center of mass of the particle distribution is investigated, and shown to have corrections in the first order of the potential curvature.

cond-mat.quant-gas↗

arXiv2021

Equilibration of the chiral asymmetry due to finite electron mass in electron-positron plasma

We calculate the rate of collisional decay of the axial charge in an ultrarelativistic electron-positron plasma, also known as the chirality flipping rate. We find that contrary to the existing estimates, the chirality flipping rate appears already in the first order in the fine-structure constant $α$ and is therefore orders of magnitude greater than previously believed. The main channels for the rapid relaxation of the axial charge are the collinear emission of a weakly damped photon and the Compton scattering. The latter contributes to the $\mathcal{O}(α)$ result because of the infrared divergence in its cross section, which is regularized on the soft scale $\sim eT$ due to the thermal corrections. Our results are important for the description of the early Universe processes (such as leptogenesis or magnetogenesis) that affect differently left- and right-chiral fermions of the Standard Model, as discussed in more details in the companion Letter.

hep-ph↗

arXiv2021

Evolution of the Primordial Axial Charge across Cosmic Times

We investigate collisional decay of the axial charge in an electron-photon plasma at temperatures 10 MeV - 100 GeV. We demonstrate that the decay rate of the axial charge is first order in the fine-structure constant $Γ_{\rm flip}\propto αm_{e}^{2}/T$ and thus orders of magnitude greater than the naive estimate which has been in use for decades. This counterintuitive result arises through infrared divergences regularized at high temperature by environmental effects. The decay of axial charge plays an important role in the problems of leptogenesis and cosmic magnetogenesis.

hep-ph↗

arXiv2018

Symmetry-restoring quantum phase transition in a two-dimensional spinor condensate

Bose Einstein condensates of spin-1 atoms are known to exist in two different phases, both having spontaneously broken spin-rotation symmetry, a ferromagnetic and a polar condensate. Here we show that in two spatial dimensions it is possible to achieve a quantum phase transition from a polar condensate into a singlet phase symmetric under rotations in spin space. This can be done by using particle density as a tuning parameter. Starting from the polar phase at high density the system can be tuned into a strong-coupling intermediate-density point where the phase transition into a symmetric phase takes place. By further reducing the particle density the symmetric phase can be continuously deformed into a Bose-Einstein condensate of singlet atomic pairs. We calculate the region of the parameter space where such a molecular phase is stable against collapse.

cond-mat.quant-gas↗

arXiv2017

Microwave control of coupling parameters in spinor alkali condensates

We propose a protocol which utilises radio frequency magnetic pulses in order to tune the effective two-particle scattering amplitudes for alkali atoms in the $F=1$ hyperfine ground state. Unlike the Feshbach resonance method, the proposed protocol preserves with controllable accuracy the global rotational symmetry in the spin space offering access to a broad region of the phase diagram of the rotationally-symmetric spinor Bose condensate. Examples of $^{41}$K and $^{7}$Li are considered and it is shown that for these atoms sufficient variation in the effective coupling constants can be achieved in order to explore phase transitions between different symmetry-broken phases of the condensate.

cond-mat.quant-gas↗

arXiv2015

Reply to "Comment on 'Kinetic theory for a mobile impurity in a degenerate Tonks-Girardeau gas'"

In our recent paper [Phys. Rev. E 90, 032132 (2014)] we have studied the dynamics of a mobile impurity particle weakly interacting with the Tonks-Girardeau gas and pulled by a small external force, $F$. Working in the regime when the thermodynamic limit is taken prior to the small force limit, we have found that the Bloch oscillations of the impurity velocity are absent in the case of a light impurity. Further, we have argued that for a light impurity the steady state drift velocity, $V_D$, remains finite in the limit $F\rightarrow 0$. These results are in contradiction with earlier works by Gangardt, Kamenev and Schecter [Phys. Rev. Lett. 102, 070402 (2009), Annals of Physics 327, 639 (2012)]. One of us (OL) has conjectured [Phys. Rev. A 91, 040101 (2015)] that the central assumption of these works - the adiabaticity of the dynamics - can break down in the thermodynamic limit. In the preceding Comment [Phys. Rev. E 92, 016101 (2015)] Schecter, Gangardt and Kamenev have argued against this conjecture and in support of the existence of Bloch oscillations and linearity of $V_D(F)$. They have suggested that the ground state of the impurity-fluid system is a quasi-bound state and that this is sufficient to ensure adiabaticity in the thermodynamic limit. Their analytical argument is based on a certain truncation of the Hilbert space of the system. We argue that extending the results and intuition based on their truncated model on the original many-body problem lacks justification.

cond-mat.quant-gas↗

arXiv2015

The fate of a gray soliton in a quenched Bose-Einstein condensate

We investigate the destiny of a gray soliton in a repulsive one-dimensional Bose-Einstein condensate undergoing a sudden quench of the non-linearity parameter. The outcome of the quench is found to depend dramatically on the ratio $η$ of the final and initial values of the speed of sound. For integer $η$ the soliton splits into exactly $2η-1$ solitons. For non-integer $η$ the soliton decays into multiple solitons and Bogoliubov modes. The case of integer $η$ is analyzed in detail. The parameters of solitons in the out-state are found explicitly. Our approach exploits the inverse scattering method and can be easily used for the similar quenches in any classical integrable system.

cond-mat.quant-gas↗

arXiv2014

Zero Mode Tunnelling in a Fractional Quantum Hall Device

Tunnelling measurements on fractional quantum Hall systems are continuing to increase in popularity since they provide a method to probe the non-Fermi liquid behaviour of fractionally charged excitations occupying the edge states of a quantum Hall system. When considering tunnelling one must resort to an effective theory and typically a phenomenological tunnelling Hamiltonian is used analogous to that used for a conventional Luttinger liquid. It is the form of this tunnelling Hamiltonian that is investigated in this work by making a comparison to an exact microscopic calculation of the zero mode tunnelling matrix elements. The computation is performed using Monte Carlo and results were obtained for various system sizes for the $ν=1/3$ Laughlin state. Here we also present a solution to overcome the phase problem experienced in Monte Carlo calculations using Laughlin-type wavefunctions. Comparing the system size dependence of the microscopic and phenomenological calculations for the tunnelling matrix elements, it was found that only for a particular type of operator ordering in the tunnelling Hamiltonian was it possible to make a good match to the numerical calculations. From the Monte Carlo data it is also clear that for any system size the electron tunnelling is always less relevant than the quasiparticle tunnelling process, supporting the idea that when considering tunnelling at a weak barrier, the electron tunnelling process can be neglected.

cond-mat.str-el↗

arXiv2014

Kinetic theory for a mobile impurity in a degenerate Tonks-Girardeau gas

A kinetic theory describing the motion of an impurity particle in a degenerate Tonks-Girardeau gas is presented. The theory is based on the one-dimensional Boltzmann equation. An iterative procedure for solving this equation is proposed, leading to the exact solution in number of special cases and to an approximate solution with the explicitly specified precision in a general case. Previously we have reported that the impurity reaches a non-thermal steady state, characterized by an impurity momentum $p_\infty$ depending on its initial momentum $p_0$. In the present paper the detailed derivation of $p_\infty(p_0)$ is provided. We also study the motion of an impurity under the action of a constant force $F$. It is demonstrated that if the impurity is heavier than the host particles, $m_i>m_h$, damped oscillations of the impurity momentum develop, while in the opposite case, $m_i<m_h$, oscillations are absent. The steady state momentum as a function of the applied force is determined. In the limit of weak force it is found to be force independent for a light impurity and proportional to $\sqrt{F}$ for a heavy impurity.

cond-mat.quant-gas↗

arXiv2014

Momentum relaxation of a mobile impurity in a one-dimensional quantum gas

We investigate the time evolution of the momentum of an impurity atom injected into a degenerate Tonks-Girardeau gas. We establish that given an initial momentum $p_0$ the impurity relaxes to a steady state with a non-vanishing momentum $p_\infty.$ The nature of the steady state is found to depend drastically on whether the masses of the impurity and the host are equal or not. This is due to multiple coherent scattering processes leading to a resonant interaction between the impurity and the host in the case of equal masses. The dependence of $p_\infty$ on $p_0$ remains non-trivial even in the limit of vanishing interaction between the impurity and host particles. In this limit $p_\infty(p_0)$ is found explicitly.

cond-mat.quant-gas↗

arXiv2014

Non-equilibrium noise in transport across a tunneling contact between $ν= 2/3$ fractional quantum Hall edges

In a recent experimental paper [1] a qualitative confirmation of the existence of upstream neutral modes at $ν= 2/3$ quantum Hall edge was reported. Using the chiral Luttinger liquid theory of quantum Hall edge we develop a quantitative model of the experiment [1]. A good quantitative agreement of our theory with the experimental data reinforces the conclusion of existence of the upstream neutral mode. Our model also enables us to extract important quantitative information about non-equilibrium processes in Ohmic and tunneling contacts from the experimental data. In particular, for $ν= 2/3$, we find a power-law dependence of the neutral mode temperature on the charge current injected from the Ohmic contact.

cond-mat.str-el↗

arXiv2011

Thermodynamics of localized magnetic moments in a Dirac conductor

We show that the magnetic susceptibility of a dilute ensemble of magnetic impurities in a conductor with a relativistic electronic spectrum is non-analytic in the inverse tempertature at $1/T\to 0$. We derive a general theory of this effect and construct the high-temperature expansion for the disorder averaged susceptibility to any order, convergent at all tempertaures down to a possible ordering transition. When applied to Ising impurities on a surface of a topological insulator, the proposed general theory agrees with Monte Carlo simulations, and it allows us to find the critical temperature of the ferromagnetic phase transition.

cond-mat.stat-mech↗

arXiv1999

Tunnelling Spectroscopy of Localized States near the Quantum Hall Edge

In the paper we dscuss experimental results of M. Grayson et al. on tunneling $I$-$V$ characteristics of the quantum Hall edge. We suggest a two step tunneling mechanism involving localized electron states near the edge, which might account for discrepancy between the experimental data and the predictions of the chiral Luttinger liquid theory of the quantum Hall edge.

cond-mat.mes-hall↗