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Grigory A. Starkov

Publications and source records attributed to Grigory A. Starkov.

14 recordsLinked to original sources
arXiv2026

Tomographic flow regime vs even-odd effect for the magnetotransport in the Corbino geometry

In two dimensions, the geometric constraints due to Pauli blocking and conservation laws lead to the even-odd effect exhibited by the electron-electron scattering lengths: electron-electron collisions are more efficient at relaxing the even angular harmonics of the distribution function than the odd ones. Inspired by a recent experiment on the magnetotransport in the Corbino disk geometry, we numerically analyze the electron flows in this geometry across all the regimes. We predict a clear signature of the even-odd effect - enhancement of the resistance sensitivity $\partial R/\partial(B^2)$ at small magnetic fields $B\rightarrow 0$. This enhancement is most prominent at the crossover from the ballistic to the tomographic regime, and gradually disappears when the temperature is further increased. Our estimates suggest that in the temperature range of the experiment, the effect should be small. This implies that the attribution of the anomalous scaling of the kinematic viscosity, that was observed in the experiment, to the even-odd effect might need more careful consideration. As a side note, we show how the method of characteristics can be extended to treat the long-lived odd harmonics, which allows one to recast the linearized Boltzmann equation as a system of integral ones.

cond-mat.mes-hall↗
arXiv2026

Characterizing all non-Hermitian degeneracies using algebraic approaches: Defectiveness and asymptotic behavior

The presence of degeneracies plays a crucial role in describing the behavior of non-Hermitian (NH) systems. In these systems, there are two key types of degeneracies: $n$-bolical degeneracies, which are analogous to Hermitian degeneracies, and various forms of exceptional points, each associated with different orders that correspond to sizes of the Jordan blocks. These types of degeneracies may coalesce at the same energy level, forming multi-block degeneracies. To understand how a multi-block degenerate NH system responds to perturbations, one should address how each types of involved degeneracies disperse. In this work, we systematically characterize the asymptotic behavior of all types of multi-block degeneracies in NH systems using a rigorous mathematical formulation. Through a range of examples, we demonstrate that our algebraic approach can facilitate the analysis of NH degeneracies in various settings relevant to experiments.

quant-ph↗
arXiv2026

Converting non-Hermitian degeneracies of any order: Hierarchies of exceptional points and degeneracy manifolds

The emergence of various types of degeneracies plays a crucial role in optimizing and engineering different physical phenomena in non-Hermitian physics. In our work, we focus on the derogatory Exceptional Points (EPs), which are characterized by multiple Jordan blocks corresponding to the same eigenvalue. We demonstrate that, under certain infinitesimal perturbations, a derogatory EP can be converted into an EP of different structure without varying the total order of degeneracy. In particular, such conversion can increase the size of the largest Jordan block and, hence, the sensitivity of the eigenspectrum to parameter variation, which is an important feature for practical applications. Furthermore, by analyzing all possible conversions, we introduce hierarchies of degeneracies of the same order that appear when perturbing non-Hermitian systems. We systematically explore hierarchies in the absence of any symmetry and when pseudo-Hermitian symmetry is present. Our study facilitates engineering various degeneracies of non-Hermitian systems, paving the way to extending the implications of non-Hermitian physics.

quant-ph↗
arXiv2026

Multi-block exceptional points in open quantum systems

Open quantum systems can be approximately described by non-Hermitian Hamiltonians (NHHs) and Liouvillian superoperators. The two approaches differ by quantum jump terms corresponding to a measurement of the system by its environment. We analyze the emergence of exceptional points (EPs) in NHHs and Liouvillian superoperators. In particular, we show how EPs in NHHs relate to a novel type of EPs -- multi-block EPs -- in the no-jump Liouvillian, i.e. the Liouvillian superoperator in absence of quantum jump terms. We further analyze how quantum jump terms modify the multi-block structure. To illustrate our general findings, we present two prime examples: qubits and qutrits coupled to additional ground state levels that serve as sinks of the population. In those examples, we can navigate through the EP block structure by a variation of physical parameters. We analyze how the dynamics of the population of the states is affected by the order of the EPs. Additionally, we demonstrate that the quantum geometric tensor serves as a sensitive indicator of EPs of different kinds.

quant-ph↗
arXiv2026

Anomalous Knudsen effect signaling long-lived modes in 2D electron gases

Proper analysis of electron collisions in two spatial dimensions leads to the conclusion, that the odd harmonics of the electron distribution function decay much slower than the even ones at finite temperatures. The number of long-lived odd harmonics quickly shrinks with increasing temperature. Focusing on a channel geometry with boundary scattering, we show that such behavior of the odd decay rates leads to a characteristic behaviour of the conductance that we dub anomalous Knudsen effect: it initially grows with temperature but then starts to decrease, forming a peak. Further increase of the temperature forces the conductance to grow again due to the Gurzhi effect, associated with the crossover from ballistic to hydrodynamic transport. The simultaneous observation of the Gurzhi dip preceded by the anomalous Knudsen peak constitutes a particular signature of the long-lived modes in 2D electron transport at low temperatures.

cond-mat.mes-hall↗
arXiv2023

Schrieffer-Wolff transformation for non-Hermitian systems: application for $\mathcal{PT}$-symmetric circuit QED

Combining non-hermiticity and interactions yields novel effects in open quantum many-body systems. Here, we develop the generalized Schrieffer-Wolff transformation and derive the effective Hamiltonian suitable for various quasi-degenerate \textit{non-Hermitian} systems. We apply our results to an exemplary $\mathcal{PT}$--symmetric circuit QED composed of two non-Hermitian qubits embedded in a lossless resonator. We consider a resonant quantum circuit as $|ω_r-Ω| \ll ω_r$, where $Ω$ and $ω_r$ are qubits and resonator frequencies, respectively, providing well-defined groups of quasi-degenerate resonant states. For such a system, using direct numerical diagonalization we obtain the dependence of the low-lying eigenspectrum on the interaction strength between a single qubit and the resonator, $g$, and the gain (loss) parameter $γ$, and compare that with the eigenvalues obtained analytically using the effective Hamiltonian of resonant states. We identify $\mathcal{PT}$--symmetry broken and unbroken phases, trace the formation of Exceptional Points of the second and the third order, and provide a complete phase diagram $g-γ$ of low-lying resonant states. We relate the formation of Exceptional Points to the additional $\mathcal{P}$-pseudo-Hermitian symmetry of the system and show that non-hermiticity mixes the "dark" and the "bright" states, which has a direct experimental consequence.

quant-ph↗
arXiv2023

Formation of Exceptional Points in pseudo-Hermitian Systems

Motivated by the recent growing interest in the field of $\mathcal{P}\mathcal{T}$-symmetric Hamiltonian systems we theoretically study the emergency of singularities called Exceptional Points ($\textit{EP}$s) in the eigenspectrum of pseudo-Hermitian Hamiltonian as the strength of Hermiticity-breaking terms turns on. Using general symmetry arguments, we characterize the separate energy levels by a topological $\mathbb{Z}_2$ index which corresponds to the signs $\pm 1$ of the eigenvalues of pseudo-metric operator $\hat ζ$ in the absence of Hermiticity-breaking terms. After that, we show explicitly that the formation of second-order $\textit{EP}$s is governed by this $\mathbb{Z}_2$-index: only the pairs of levels with $\textit{opposite}$ index can provide second-order $\textit{EP}$s. Our general analysis is accompanied by a detailed study of $\textit{EP}$s appearance in an exemplary $\mathcal{P}\mathcal{T}$-symmetric pseudo-Hermitian system with parity operator in the role of $\hat ζ$: a transverse-field Ising spin chain with a staggered imaginary longitudinal field. Using analytically computed parity indices of all the levels, we analyze the eigenspectrum of the model in general, and the formation of third-order $\textit{EP}$s in particular

quant-ph↗
arXiv2022

Quantum phase transitions in non-Hermitian $\mathcal{P}\mathcal{T}$-symmetric transverse-field Ising spin chains

We present a theoretical study of quantum phases and quantum phase transitions occurring in non-Hermitian $\mathcal{P}\mathcal{T}$-symmetric superconducting qubits chains described by a transverse-field Ising spin model. A non-Hermitian part of the Hamiltonian is implemented via imaginary staggered \textit{longitudinal } magnetic field, which corresponds to a local staggered gain and loss terms. By making use of a direct numerical diagonalization of the Hamiltonian for spin chains of a finite size $N$, we explore the dependencies of the energy spectrum, including the energy difference between the first excited and the ground states, the spatial correlation function of local polarization ($z$-component of local magnetization) on the adjacent spins interaction strength $J$ and the local gain (loss) parameter $γ$. A scaling procedure for the coherence length $ξ$ allows us to establish a complete quantum phase diagram of the system. We obtain two quantum phases for $J<0$, namely, $\mathcal{P}\mathcal{T}$-symmetry broken antiferromagnetic state and $\mathcal{P}\mathcal{T}$-symmetry preserved paramagnetic state, and the quantum phase transition line between them is the line of exception points. For $J>0$ the $\mathcal{P}\mathcal{T}$-symmetry of the ground state is retained in a whole region of parameter space of $J$ and $γ$, and a system shows \textit{two} intriguing quantum phase transitions between ferromagnetic and paramagnetic states for a fixed parameter $γ> 1$. We also provide the qualitative quantum phase diagram $γ-J$ derived in the framework of the Bethe-Peierls approximation that is in a good accord with numerically obtained results.

quant-ph↗
arXiv2021

Slowly decaying real-time oscillations in instanton crystal

Instanton crystal is a fascinating phase which is encountered when the minimum of the free energy corresponds to a configuration with an imaginary-time-dependent order parameter in the form of a chain of alternating instantons and anti-instantons. We present the results of the investigation of the real-time correlation functions of the order parameter in the instanton crystal phase. In order to obtain the correlation functions in real-time, we formulate an original method of analytic continuation from imaginary times, which is easily adapted into an efficient numerical scheme for the computations. The resulting correlation functions exhibit non-trivial slowly decaying oscillations in real-time, which is reminiscent of prethermal time crystals.

cond-mat.str-el↗
arXiv2020

Phase transition into Instanton Crystal

We propose a class of models exhibiting instanton crystal phase. In this phase, the minimum of the free energy corresponds to a configuration with an imaginary-time-dependent order parameter in a form of a chain of alternating instantons and antiinstantons. The resulting characteristic feature of this state is that the average of the order parameter over the imaginary time vanishes. In order to study the model in a broad region of parameters of the model quantitatively, and prove the existence of the instanton crystal phase, we develop an efficient numerical scheme, suitable for the exact treatment of the proposed models. In a certain limit, results demonstrating the existence of the instanton crystal phase are obtained also analytically. The numerical study of the model shows that there is a phase transition between the instanton crystal and the state with the imaginary-time-independent order parameter.

cond-mat.str-el↗
arXiv2019

Free induction decays in nuclear spin-1/2 lattices with small number of interacting neighbors: the cases of silicon and fluorapatite

Nuclear spin-1/2 lattices where each spin has a small effective number of interacting neighbors represent a particular challenge for first-principles calculations of free induction decays (FIDs) observed by nuclear magnetic resonance (NMR). The challenge originates from the fact that these lattices are far from the limit where classical spin simulations perform well. Here we use the recently developed method of hybrid quantum-classical simulations to compute nuclear FIDs for $^{29}$Si-enriched silicon and fluorapatite. In these solids, small effective number of interacting neighbors is either due to the partition of the lattice into pairs of strongly coupled spins (silicon), or due to the partition into strongly coupled chains (fluorapatite). We find a very good overall agreement between the hybrid simulation results and the experiments. In addition, we introduce an extension of the hybrid method, which we call the method of "coupled quantum clusters". It is tested on $^{29}$Si-enriched silicon and found to exhibit excellent performance.

cond-mat.mes-hall↗
arXiv2018

Classical spin simulations with a quantum two-spin correction

Classical simulations of high-temperature nuclear spin dynamics in solids are known to accurately predict relaxation for spin 1/2 lattices with a large number of interacting neighbors. Once the number of interacting neighbors becomes four or smaller, classical simulations lead to noticeable discrepancies. Here we attempt to improve the performance of the classical simulations by adding a term representing two-spin quantum correlations. The method is tested for a spin-1/2 chain. It exhibits good performance at shorter times, but, at longer times, it is hampered by a singular behavior of the resulting equations of motion.

cond-mat.str-el↗
arXiv2018

Hybrid quantum-classical method for simulating high-temperature dynamics of nuclear spins in solids

First-principles calculations of high-temperature spin dynamics in solids in the context of nuclear magnetic resonance (NMR) is a long-standing problem, whose conclusive solution can significantly advance the applications of NMR as a diagnostic tool for material properties. In this work, we propose a new hybrid quantum-classical method for computing NMR free induction decay(FID) for spin $1/2$ lattices. The method is based on the simulations of a finite cluster of spins $1/2$ coupled to an environment of interacting classical spins via a correlation-preserving scheme. Such simulations are shown to lead to accurate FID predictions for one-, two- and three-dimensional lattices with a broad variety of interactions. The accuracy of these predictions can be efficiently estimated by varying the size of quantum clusters used in the simulations.

cond-mat.stat-mech↗