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Emil A. Yuzbashyan

Publications and source records attributed to Emil A. Yuzbashyan.

At least 19 recordsLinked to original sources
arXiv2026

Amplitude mode in Eliashberg superconductors

In the BCS theory of superconductivity the amplitude (Higgs) mode is degenerate with the pair-breaking threshold: its frequency coincides with $2Δ$, so it is an edge singularity rather than a true collective mode. This is why after a sudden weak perturbation at $t=0$ its oscillations decay algebraically as $1/\sqrt{t}$. We show that the retardation effects due to the phonon dynamics in the strong-coupling theory lift this degeneracy. The Higgs mode detaches from the pair-breaking edge $2Δ_g$, set by the spectral gap, and becomes a sharp subgap excitation. We determine its frequency from the longitudinal pair susceptibility evaluated directly on the real frequency axis, using the Eilenberger equations for Migdal--Eliashberg theory with the Einstein phonon spectrum. The response of the mass renormalization supplies at least two fifths of the displacement, and possibly all of it: with it switched off, the binding falls below the resolution of the calculation. Its consequences, however, are significant because a percent-level shift transfers about a quarter of the spectral weight of the amplitude channel out of the two-quasiparticle continuum into a discrete energy level. What experiment sees is therefore not the displacement itself but its consequence: amplitude oscillations that persist instead of decaying as $1/\sqrt{t}$.

cond-mat.supr-con↗
arXiv2026

Fluctuation theorems and exact multi-allele fixation probabilities

A mutant gene that appears in a finite population will, in the long run, either disappear from it or become fixed, so that all members of the population will carry a copy of the mutant gene. Determining the fixation probability of a mutant gene is thus a prerequisite for modeling evolutionary dynamics in finite populations. Within the diffusion theory framework, the mutant's competition with the wild-type genes is described by the closed-form solution of a one-dimensional backward Kolmogorov equation for the mutant fixation probability, derived by Motoo Kimura in 1962. However, in asexual populations the rate of adaptation and the relative importance of alternative evolutionary pathways are shaped by clonal interference - the competition between several lineages arising from distinct beneficial or deleterious mutations. Quantitative descriptions of clonal interference require computing fixation probabilities in populations where multiple alleles are present simultaneously - a formidable mathematical problem which amounts to solving a multi-dimensional backward Kolmogorov equation. Here, we employ fluctuation theorems (a set of exact equalities in non-equilibrium statistical mechanics) in order to re-derive Kimura's fixation probability formula. When extended to multi-allele systems, fluctuation theorems provide a constraint which must be satisfied by any valid set of fixation probabilities. Moreover, we present a recursive analytical solution of the multi-allele fixation probability problem. We use our formalism to study the fate of a novel beneficial mutation in a clonal interference scenario, discovering substantial deviations between our exact treatment and the mean-field approximation in which the target mutation competes with a single effective genotype. Our formalism can be used to replace both explicit simulations and approximate analytical results in models of asexual evolution.

q-bio.PE↗
arXiv2026

Stability Analysis of Superconductivity in $\textit{P6/mmm}$-LaSc$_2$H$_{24}$ and its Experimental Reproducibility from La-Sc Alloys

In this work, we analyze the feasibility of room-temperature superconductivity in the lanthanum-scandium hydride $\textit{P6/mmm}$-LaSc$_2$H$_{24}$. We demonstrate that the electron-phonon coupling calculations performed using the $σ$-broadening of the double $δ$-function at the Fermi surface lead to a very strong dependence of $\textit{T$_c$}(σ)$ on the arbitrary $σ$, whereas the tetrahedral method for the electron-phonon interaction is free from this drawback and leads to $\textit{T$_c$}$ > 300 K at 300 GPa in agreement with previous predictions. By analyzing the stability of the metallic state of LaSc$_2$H$_{24}$ at 250-300 GPa, we show that this compound is at the edge of the stability region ($ξ$ = 0.54), similar to $\textit{fcc}$ LaH$_{10}$ at 140-150 GPa. Seven experimental attempts to synthesize LaSc$_2$H$_{24}$ at 250-280 GPa starting from the (La,Sc$_2$) alloy are unsuccessful and indicate the absence of even traces of superconductivity at 245-300 K in all the resulting La-Sc-H hydrides. The method for preparing the precursor by simultaneous deposition of La and Sc metals may be a key factor for the successful synthesis of LaSc$_2$H$_{24}$.

cond-mat.supr-con↗
arXiv2026

Weyl's Relations, Integrable Matrix Models and Quantum Computation

Starting from a generalization of Weyl's relations in finite dimension $N$, we show that the Heisenberg commutation relations can be satisfied in a specific $N-1$ dimensional subspace, and display a linear map for projecting operators to this subspace. This setup is used to construct a hierarchy of parameter-dependent commuting matrices in $N$ dimensions. This family of commuting matrices is then related to Type-1 matrices representing quantum integrable models. The commuting matrices find an interesting application in quantum computation, specifically in Grover's database search problem. Each member of the hierarchy serves as a candidate Hamiltonian for quantum adiabatic evolution and, in some cases, achieves higher fidelity than standard choices -- thus offering improved performance.

quant-ph↗
arXiv2025

The measurement-induced phase transition in strongly disordered spin chains

We investigate the dynamics of strongly disordered spin chains in the presence of random local measurements. By studying the transverse-field Ising model with a site-dependent random longitudinal field and an effective $l$-bit many-body localized Hamiltonian, we show that the prethermal and MBL regimes are unstable to local measurements along any direction. Any non-zero measurement density induces a volume-law entangled phase with a subsequent phase transition into an area-law state as the measurement rate is further increased. The critical measurement rate $p_c$, where the transition occurs, is exponentially small in the strength of disorder $W$ and the average overlap between the measurement operator and the local integrals of motion $O$ as $p_c \sim \exp[-αW/(1-O^2)]$. In the measurement-induced volume-law phase, the saturation time scales as $t_s \sim L $, contrasting the exponentially slow saturation $t_s \sim e^{aL}$ in the prethermal and MBL regimes at $p = 0$.

cond-mat.dis-nn↗
arXiv2025

Trotter transition in BCS pairing dynamics

We study universal aspects of thermalization induced by Trotterization, a procedure routinely used in gate-based quantum computation. We use the reduced-BCS model -- quantum integrable with a classically integrable mean-field limit -- where the effects of Trotter chaos are expected to be particularly stark. The resulting Trotterized chaotic dynamics is characterized by its Lyapunov spectrum and rescaled Kolmogorov-Sinai entropy. The chaos quantifiers depend on the Trotterization time step $τ$. We observe a Trotter transition at a finite step value $τ_c \approx \sqrt{N}$. While the dynamics is weakly chaotic for time steps $τ\ll τ_c$, the regime of large Trotterization steps is characterized by short temporal correlations. We derive two different scaling laws for the two different regimes by numerically fitting the maximum Lyapunov exponent data. The scaling law of the large \(τ\) limit agrees well with the one derived from the kicked top map. Beyond its relevance to current quantum computers, our work opens new directions -- such as probing observables like the Loschmidt echo, which lie beyond standard mean-field description -- across the Trotter transition we uncover.

quant-ph↗
arXiv2025

Turning Down the Noise: Power-Law Decay and Temporal Phase Transitions

We determine the late-time dynamics of a generic spin ensemble with inhomogeneous broadening - equivalently, qubits with arbitrary Zeeman splittings - coupled to a dissipative environment with strength decreasing as $1/t$. The approach to the steady state follows a power law, reflecting the interplay between Hamiltonian dynamics and vanishing dissipation. The decay exponents vary non-analytically with the ramp rate, exhibiting a cusp singularity, and $n$-point correlation functions factorize into one- and two-point contributions. Our exact solution anchors a universality class of open quantum systems with explicitly time-dependent dissipation.

quant-ph↗
arXiv2025

Fundamental limits on the electron-phonon coupling and superconducting $T_c$

Fundamental upper bounds on the electron-phonon interaction strength and superconducting transition temperature $T_c$ in metals are established based on the intrinsic instability of the equilibrium between electrons and the crystal lattice under strong interaction. This instability explains why observed electron-phonon coupling constants are limited to $λ\lesssim 4$. The theory also accounts for the mechanism of metastable superconductivity with enhanced $T_c$, which emerges near the instability threshold. Based on theoretical analysis and comparison with experimental data, room-temperature phonon-mediated superconductivity is found to be feasible exclusively in hydrogen compounds.

cond-mat.supr-con↗
arXiv2025

Higher spin Richardson-Gaudin model with time-dependent coupling: Exact dynamics

We determine the exact asymptotic many-body wavefunction of a spin-$s$ Richardson-Gaudin model with a coupling inversely proportional to time, for time evolution starting from the ground state at $t = 0^+$ and for arbitrary $s$. Contrary to common belief, the resulting wavefunction cannot be derived from the spin-$1/2$ case by merging spins, but instead requires independent treatment for each spin size. The steady state is non-thermal and, in contrast to the spin-$1/2$ case, does not conform to a natural Generalized Gibbs Ensemble. We show that mean-field theory is exact for any product of a finite number of spin operators on different sites. We discuss how these findings can be probed in cavity QED and trapped ion experiments.

quant-ph↗
arXiv2025

Bounds on $T_c$ in the Eliashberg theory of Superconductivity. II: Dispersive phonons

The standard Eliashberg theory of superconductivity is studied, in which the effective electron-electron interactions are mediated by generally dispersive phonons, with Eliashberg spectral function $α^2 F(ω)\geq 0$ that is $\proptoω^2$ for small $ω>0$ and vanishes for large $ω$. The Eliashberg function also defines the electron-phonon coupling strength $λ:= 2 \int_0^\infty\frac{α^2 F(ω)}ωdω$. Setting $\frac{2α^2 F(ω)}ωdω=: λP(dω)$, formally defining a probability measure $P(dω)$ with compact support, and assuming as usual that the phase transition between normal and superconductivity coincides with the linear stability boundary $\mathscr{S}_{\!c}$ of the normal region against perturbations toward the superconducting region, it is shown that $\mathscr{S}_{\!c}$ is a graph of a function $Λ(P,T)$ that is determined by a variational principle: if $(λ,P,T)\in\mathscr{S}_{\!c}$, then $λ= 1/\mathfrak{k}(P,T)$, where $\mathfrak{k}(P,T)>0$ is the largest eigenvalue of a compact self-adjoint operator $\mathfrak{K}(P,T)$ on $\ell^2$ sequences constructed in the paper. Given $P$, sufficient conditions on $T$ are stated under which the map $T\mapsto λ= Λ(P,T)$ is invertible. For sufficiently large $λ$ this yields: (i) the existence of a critical temperature $T_c$ as function of $λ$ and $P$; (ii) a sequence of lower bounds on $T_c(λ,P)$ that converges to $T_c(λ,P)$. Also obtained is an upper bound on $T_c(λ,P)$. It agrees with the asymptotic form $T_c(λ,P) \sim C \sqrt{\langle ω^2\rangle} \sqrtλ$ valid for $λ\sim\infty$, given $P$, though with a constant $C$ that is a factor $\approx 2.034$ larger than the sharp constant. Here, $\langleω^2\rangle := \int_0^\infty ω^2 P(dω)$.

math-ph↗
arXiv2025

Instability of metals with respect to strong electron-phonon interaction

We show that thermal equilibrium between conduction electrons and phonons becomes kinetically unstable when the renormalized electron-phonon coupling exceeds a certain threshold. We prove that negative electronic specific heat, $C_\mathrm{el} < 0$, is sufficient to trigger the instability. Specifically, the instability sets in as soon as the quasiparticle weight becomes negative over a range of energies, even before $C_\mathrm{el}$ turns negative. This is an inherently nonequilibrium phenomenon, occurring prior to the formation of any equilibrium phase. Depending on the system, it can proceed along different pathways, ultimately resulting in a structural transition to an insulating or metallic state.

cond-mat.str-el↗
arXiv2025

Knizhnik-Zamolodchikov equations and integrable hyperbolic Landau-Zener models

We study the relationship between integrable Landau-Zener (LZ) models and Knizhnik-Zamolodchikov (KZ) equations. The latter are originally equations for the correlation functions of two-dimensional conformal field theories, but can also be interpreted as multi-time Schrödinger equations. The general LZ problem is to find probabilities of tunneling from eigenstates at $t=t_\text{in}$ to eigenstates at $t\to+\infty$ for an $N\times N$ time-dependent Hamiltonian $\hat H(t)$. A number of such problems are exactly solvable in the sense that their tunneling probabilities are elementary functions of Hamiltonian parameters. Recently, it has been proposed that exactly solvable LZ models of this type map to KZ equations. Here we use this connection to identify and solve a class of integrable LZ models with hyperbolic time dependence, $\hat H(t)=\hat A+\hat B/t$, for $N=2, 3$, and $4$, where $\hat A$ and $\hat B$ are time-independent matrices.

cond-mat.stat-mech↗
arXiv2025

Bounds on $T_c$ in the Eliashberg theory of Superconductivity. I: The $γ$-model

Using the recent reformulation for the Eliashberg theory of superconductivity in terms of a classical interacting Bloch spin chain model, rigorous upper and lower bounds on the critical temperature $T_c$ are obtained for the $γ$ model -- a version of Eliashberg theory in which the effective electron-electron interaction is proportional to $(g/|ω_n-ω_m|)^γ$, where $ω_n-ω_m$ is the transferred Matsubara frequency, $g>0$ a reference energy, and $γ>0$ a parameter. The rigorous lower bounds are based on a variational principle that identifies $(T_c/g)^γ$ with the largest (positive) eigenvalue of an explicitly constructed compact, self-adjoint operator $\mathfrak{G}(γ)$. These lower bounds form an increasing sequence that converges to $T_c(g,γ)$. The upper bound on $T_c(g,γ)$ is based on fixed point theory, proving linear stability of the normal state for $T$ larger than the upper bound on $T_c(g,γ)$.

math-ph↗
arXiv2025

Bounds on $T_c$ in the Eliashberg theory of Superconductivity. III: Einstein phonons

The dispersionless limit of the standard Eliashberg theory of superconductivity is studied. The effective electron-electron interactions are mediated by Einstein phonons of frequency $Ω>0$, equipped with electron-phonon coupling strength $λ$. This allows for a detailed evaluation of the general results on $T_c$ for phonons with non-trivial dispersion relation, obtained in a previous paper, (II), by the authors. The variational principle for the linear stability boundary $\mathscr{S}_{\!c}$ of the normal state region against perturbations toward the superconducting region, obtained in (II), simplifies as follows: If $(λ,Ω,T)\in\mathscr{S}_{\!c}$, then $λ= 1/\mathfrak{h}(\varpi)$, where $\varpi:=Ω/2πT$, and where $\mathfrak{h}(\varpi)>0$ is the largest eigenvalue of a compact self-adjoint operator $\mathfrak{H}(\varpi)$ on $\ell^2$ sequences; $\mathfrak{H}(\varpi)$ is the dispersionless limit $P(dω)\toδ(ω-Ω)dω$ of the operator $\mathfrak{K}(P,T)$ of (II). It is shown that when $\varpi \leq \sqrt{2}$, then the map $\varpi\mapsto\mathfrak{h}(\varpi)$ is invertible. For $λ>0.77$ this yields: (i) the existence of a critical temperature $T_c(λ,Ω) = Ωf(λ)$; (ii) a sequence of lower bounds on $f(λ)$ that converges to $f(λ)$. Also obtained is an upper bound on $T_c(λ,Ω)$, which agrees with the asymptotic behavior $T_c(λ,Ω) \sim C Ω\sqrtλ$ for $λ\sim\infty$, given $Ω$, though with $C\approx 2.034 C_\infty$, where $C_\infty := \frac{1}{2π}\mathfrak{k}(2)^\frac12 =0.1827262477...$ is the optimal constant, and $\mathfrak{k}(γ)>0$ the largest eigenvalue of a compact self-adjoint operator for the $γ$ model, determined in the first paper, (I), on $T_c$ by the authors.

cond-mat.supr-con↗
arXiv2025

Nontrivial saddle points for spectral form factors of flat band superconductors

We derive the spectral form factor of a flat band superconductor in two different ways. In the first approach, we diagonalize the Hamiltonian of this system exactly and numerically sum over the exact eigenstates to find the spectral form factor. In the second approach, we use mean field theory to evaluate the same spectral form factor. We demonstrate that both methods produce the same answer. Mean field theory for spectral form factors possesses features not previously seen in the theory of superconductivity, in particular complex gap functions and non-Hermitian effective Hamiltonians. We explicitly show that these features are indeed necessary to obtain the correct spectral form factor.

cond-mat.supr-con↗
arXiv2024

Dynamical chaos in the integrable Toda chain induced by time discretization

We use the Toda chain model to demonstrate that numerical simulation of integrable Hamiltonian dynamics using time discretization destroys integrability and induces dynamical chaos. Specifically, we integrate this model with various symplectic integrators parametrized by the time step $τ$ and measure the Lyapunov time $T_Λ$ (inverse of the largest Lyapunov exponent $Λ$). A key observation is that $T_Λ$ is finite whenever $τ$ is finite but diverges when $τ\rightarrow 0$. We compare the Toda chain results with the nonitegrable Fermi-Pasta-Ulam-Tsingou chain dynamics. In addition, we observe a breakdown of the simulations at times $T_B \gg T_Λ$ due to certain positions and momenta becoming extremely large (``Not a Number''). This phenomenon originates from the periodic driving introduced by symplectic integrators and we also identify the concrete mechanism of the breakdown in the case of the Toda chain.

nlin.CD↗
arXiv2023

Integrable mappings for noncommuting objects

We construct hierarchies of integrable systems invariant under the two-dimensional Darboux-Toda mapping for noncommuting objects, thus generalizing to the noncommutative case the integrable mapping approach to nonlinear dynamical systems. Besides the usual setup with one time and two space dimensions, we consider the case when the unknown functions also depend on two Grassman variables.

hep-th↗