arXiv subjects

Miguel Tierz

Publications and source records attributed to Miguel Tierz.

At least 19 recordsLinked to original sources

arXiv2026

Equal-charge projection of the $\mathcal{N}=4$ index: exact large-$N$ formula and finite-rank $U(3)$ coefficients

The equal-charge branch of supersymmetric rotating AdS$_5$ black holes has $Q_1=Q_2=Q_3$. The corresponding microcanonical sector of the $\mathcal{N}=4$ superconformal index is obtained by projecting to equal charges, or equivalently by extracting the constant term in the two charge-difference fugacities. We prove that for the large-$N$ multigraviton sector the projected index factorizes exactly as \[ \mathcal{I}^{\rm eqQ}_\infty(x,p) =\prod_{k\ge1}(1-p^kx^{3k})(1-p^{-k}x^{3k}) \sum_{n\ge0}\mathsf{p}(n)^3x^{6n}, \] where $\mathsf{p}(n)$ is the partition function. This factorization gives, for every spin sector, an explicit onset energy below which the large-$N$ coefficient is zero. Exact $U(3)$ computations show that finite-rank coefficients can nevertheless appear at energies where the large-$N$ coefficient vanishes, including beyond the classical $U(3)$ black-hole bound. We also determine the full line $j=6J_R+6$. In particular, with $j^*(J_R)$ denoting this large-$N$ onset energy, \[ d_3^{\rm eqQ}(87,\tfrac{27}{2})=1, \qquad j^*(\tfrac{27}{2})-87=1554, \] and the first giant-graviton sector already contributes one unit at this point. All coefficients are coefficients of the $(-1)^F$-graded index, not positive degeneracies. The main conclusion is that the high-spin tail survives the exact equal-charge projection.

hep-th↗

arXiv2026

Exact Schwarzian Metric Factor and Holographic Wilson-Loop Screening

We evaluate exactly the radial metric factor $h(\zeta)$ generated by Schwarzian averaging in the AdS$_2$ throat of an extremal Reissner--Nordstr\"om AdS$_5$ black brane. The result is a Gaussian integral against $\coth(\pi y)$, valid at all radial depths, which Mordell's identity turns into an exact Appell--Lerch $q/q^\ast$-series representation. The dual series identifies the nonperturbative scale $e^{-\pi^2 C/\zeta}$ missed by any finite near-boundary truncation. The third parametric derivative required by the evaluation generates the quasimodular Eisenstein series $E_2$, absent from the classical Mordell identity. From the integral representation we prove that $\mathcal{G}_0(\zeta):=h(\zeta)/\zeta^2$ is completely monotone and hence has no interior minimum, so any confining minimum produced by a finite near-boundary truncation is an artifact. We also compute the exact relative variance of the Schwarzian kernel, which makes the averaged-metric approximation error quantitative and shows that the absence of a confining minimum is robust across moment-based effective geometries. Applied to the temporal rectangular Wilson loop, the exact throat gives algebraic screening, $E(L)\sim -\kappa_{\rm IR}/L^2$, the Wilson-loop diagnostic of the semi-local quantum-liquid IR of the extremal RN brane. A numerical check in a simple matched geometry confirms that the screened saddle is the dominant string configuration, and an exact-versus-truncated force comparison shows that the apparent constant-force regime of the fourth-order truncation is not a feature of the exact geometry.

hep-th↗

arXiv2026

Inter-harmonic ratio structure and saturation of Bernstein modes in graphene

Bernstein modes (BM) in graphene are finite-wavevector magnetoplasmons excited by contact near fields, whereas ordinary cyclotron resonance (CR) probes $q\approx0$. We derive the BM peak absorption in the quasiclassical ballistic regime and show that it factorizes into a launch spectrum, Bernstein-mode splitting, turning-point enhancement, and residual dielectric-response factor. At fixed excitation frequency, BM overtones ($n\ge2$) are sampled, to leading order, at the same momentum $q\simeq\omega/v_F$. Smooth launch and screening factors therefore cancel in inter-harmonic peak ratios, yielding $I_n/I_m\simeq m/n$, modified by linewidth corrections and one residual response ratio for each harmonic pair. In smooth-launcher synthetic tests, noisy full-$q$ spectra recover the residual ratio within errors: moderate launcher/dielectric misspecification within this benchmark family shifts it by only $\sim\!1$--$2\%$, whereas linewidth assumptions shift it by $\sim\!10$--$30\%$. The same factorization connects low-power amplitudes to nonlinear saturation. If BM harmonics share the same cooling region and bolometric readout, the low-power slope times onset intensity is harmonic independent, while BM and CR power sweeps obey distinct normalized saturation curves with linewidth scalings $\Gamma^{-1/2}$ and $\Gamma^{-1}$.

cond-mat.mes-hall↗

arXiv2026

BPS spectra of $\operatorname{Tr}[\Psi^p]$ matrix models for odd $p$

We study the BPS cohomology and Hamiltonian of a model built from an $N\times N$ matrix $\Psi$ of complex fermions, with supercharge $Q_p={\rm Tr}(\Psi^p)$ for odd $p\ge3$. Numerical calculations give the BPS multiplicity at every fermion number for $(p,N)=(5,3),(5,4),(5,5),(7,4)$, and through fermion number six at $(7,5)$. In $Z_{BPS}^{(p,N)}(x)=\sum_Rh_Rx^R$, $x$ records fermion number and $h_R$ counts BPS states in sector $R$. In each of the four cases computed at every fermion number, factoring out the lowest power of $x$ leaves a polynomial divisible by a positive power of $p$ and by $(1+x)^N$. The quotient by these factors has nonnegative integer coefficients. Exact decoupling of ${\rm Tr}\Psi$ and the Euler characteristic prove divisibility by $(1+x)^2$. Pairing sectors of complementary fermion number gives a third factor when $N$ is odd. For odd $p\le2N-1$, the only range in which $Q_p$ can be nonzero, the same pairing proves the corresponding rank symmetry for $Q_p$. The additional factors required to reach $(1+x)^N$ remain conjectural in general. Evaluating at $x=1$ gives the total BPS count $Z_{BPS}^{(p,N)}(1)$. For each fixed odd $p$, the Witten indices imply that, for any sequence of matrix sizes $N_j\to\infty$ along which $N_j^{-2}\log Z_{BPS}^{(p,N_j)}(1)$ converges, its limit lies in $[\log(2\cos\frac{\pi}{2p}),\log 2]$. After dividing the Hamiltonian by $p^2$, normal ordering gives an alternating sum of operators $K_k$, with $K_k$ containing $k$ creation and $k$ annihilation operators. We obtain exact formulas for $K_0,K_1,K_2$ when $p=5$ and $N\ge3$. Only $K_3,K_4$ can contain spectral information beyond the number of traceless fermions and the quadratic Casimir. At $N=3$, the Hodge star maps the invariant cubic form to the quintic form up to scale, so all five terms commute. Calculations with integer matrices give nonzero commutators in the reported $N=4$ sectors.

hep-th↗

arXiv2026

Amplitudes of Hall field-induced resistance oscillations with a two-harmonic density of states

We derive explicit strong-field asymptotics for the normalized differential resistance in Hall field-induced resistance oscillations (HIRO) within the Vavilov-Aleiner-Glazman kinetic framework. For a single-harmonic density of states, the leading oscillation amplitude is set by the full backscattering rate $1/\tau(\pi)$. Extending the theory to a two-harmonic density of states, we show that the off-diagonal mixed kernel $\gamma_{12}$ admits an exact single-integral representation, from which the strong-field asymptotics follow directly. The resulting odd harmonics, notably $m=1$ and $m=3$, have coefficients determined by combinations of $1/\tau(0)$ and $1/\tau(\pi)$, while the leading $m=2$ amplitude remains unchanged. On exact-kernel mock data generated and fit within the same model, with $\tau_{\rm tr}$ and $\tau_{\rm in}$ held fixed, the resulting extraction protocol recovers $\tau_q$, $\tau(\pi)$, and -- when the $m=1,3$ harmonics are resolved -- $\tau(0)$ to sub-percent accuracy, with $\tau(0)$ providing a consistency check on the disorder description.

cond-mat.mes-hall↗

arXiv2026

Entanglement in the open XX chain: R\'enyi oscillations, hard-edge crossover, and symmetry resolution

We derive closed-form asymptotic formulas for the R\'enyi entanglement entropies of the open XX spin-$1/2$ chain by mapping the underlying determinant of the boundary correlation matrix (which has Toeplitz-plus-Hankel structure) to a Hankel determinant with a positive weight whose large-size asymptotics follow from known Riemann--Hilbert results. An explicit evaluation of the Szeg\H{o} function yields the leading $2k_F$ oscillatory amplitude and phase. A single variable $s = 2\ell \sin(k_F/2)$ organizes the hard-edge crossover as the Fermi momentum approaches the band edge: the oscillation envelope obeys $s^{\pm1/\alpha}$ power laws and $\ln s$ is the natural leading logarithm for a clean data collapse. For detached blocks the oscillatory amplitude is numerically consistent with a factorization through the conformal cross-ratio. The same framework recovers the open-boundary-condition (OBC) equipartition offset $-\tfrac{1}{2}\log\log\ell$ for symmetry-resolved entropies, together with the known halving of the Gaussian width relative to the periodic chain.

cond-mat.stat-mech↗

arXiv2026

Edge universality in Floquet sideband spectra

We show that, for non-interacting fermions under a monochromatic phase drive (Tien--Gordon regime), the outgoing sideband occupations at a sharp Fermi edge are governed by the discrete Bessel kernel -- an exact result at any drive amplitude~$A$. In the large-amplitude regime the edge of this kernel converges, on the $A^{1/3}$ scale, to the Airy kernel of random matrix theory. This universality has a direct transport consequence: the deficit of the photo-assisted shot-noise slope from its high-bias plateau collapses onto the Airy-kernel diagonal. The derivation rests on a bridge between the linear detection chain and the Floquet scattering matrix: commensurate gating isolates a single coherence-order block of the one-body correlator. We identify the crossover temperature below which the Airy scaling is sharp, extend the analysis to biased two-terminal occupations, and argue that multi-tone drives make Pearcey-kernel cusps accessible in Floquet--Sambe space.

cond-mat.mes-hall↗

arXiv2025

Finite Gauss-Sum Modular Kernels: Scalar Gap and a Pure AdS$_3$ Gravity No-Go Theorem

We obtain closed-form expressions for the $ST^nS$ modular kernels of non-rational Virasoro CFTs and use them to construct fully analytic modular-bootstrap functionals. At rational width $\tau$, the Mordell integrals in these kernels reduce to finite quadratic Gauss sums of $\operatorname{sech}/\sec$ profiles with explicit Weil phases, furnishing a canonical finite-dimensional real basis for spectral kernels. From this basis we build finite-support "window" functionals with $\Phi(0)=1$ and $\Phi(p)>0$ on a prescribed low-momentum interval. Applied to the scalar channel of the $ST^1S$ kernel, these functionals yield a rigorous analytic bound on the spinless gap. As a second application we prove an analytic no-go theorem for pure AdS$_3$ gravity: no compact, unitary, Virasoro-only CFT$_2$ can have a primary gap above $\Delta_{\rm BTZ}=(c-1)/12$, because a strictly positive "Mordell surplus" in the odd-spin $ST$ kernel forces an odd-spin primary below $\Delta_{\rm BTZ}$.

hep-th↗

arXiv2025

Integrable Contour Kernels in Discrete $\beta=1,4$ Ensembles, Universality and Kuznetsov Multipliers

We obtain explicit double-contour representations for the correlation kernels of the discrete orthogonal ($\beta=1$) and symplectic ($\beta=4$) random matrix ensembles with Meixner, Charlier, and Krawtchouk weights. A single Cauchy--difference--quotient composition identity expresses all $\beta=1,4$ blocks in terms of the projection kernel and bounded rational multipliers. From these formulas we give short steepest-descent proofs of bulk and edge universality (sine/Airy/Bessel) with uniform error control, an explicit Meixner$\to$Laguerre hard-edge crossover, and a first $A^{-1}$ correction that follows directly from the integrable structure. Finally, we show that Archimedean Kuznetsov tests splice into the Pfaffian kernels by a bounded holomorphic symbol acting in the contour variable; the symbol enters only through the same Cauchy difference--quotient, so the leading sine/Airy/Bessel limits persist and the $A^{-1}$ term again comes from linearizing at the saddle(s).

math-ph↗

arXiv2025

Radial selection rule for the breathing mode of a harmonically trapped gas

Within a fixed hyperangular channel $s>0$ of a harmonically trapped system, the $1/R^2$ perturbation is absorbed exactly into a shift of the channel parameter, $s\to s_\eta$, so the single-channel model remains a harmonic oscillator with a shifted inverse-square term: radial gaps stay at $2\hbar\omega$ exactly and no monopole spectral weight appears at forbidden frequencies at any order. The first-order cancellation is also proved independently by a compact algebraic argument in which the ket and bra contributions cancel pairwise; this is the main new result. Substituting single-channel quantities into the established $m_1/m_{-1}$ sum-rule bound yields $Q^{-1}$ scaling of the sum-rule estimate ($Q\equiv 2q+s+1$, $q$ the radial quantum number) with an explicit coefficient; its finite-temperature average has a low-$T$ plateau and a $1/T$ high-$T$ tail. All results hold for any real $s>0$. The Laguerre polynomial identities extend formally to three dimensions, but exact 3D results show $q$-dependent contact corrections along $SO(2,1)$ ladders, so the physical interpretation there requires a separate derivation.

cond-mat.quant-gas↗

arXiv2025

Work statistics of sudden Quantum quenches: A random matrix theory perspective on Gaussianity and its deviations

We show that, for sudden quenches, the work distribution reduces to the statistics of traces of powers of Haar unitaries, which are random unitary matrices drawn uniformly from the unitary group. For translation-invariant quadratic fermionic chains with interactions extending to $m$ neighbors and periodic boundary conditions, the Loschmidt amplitude admits a unitary matrix-model / Toeplitz representation, which yields a work variable of the form $W=\sum_{r\le m} a_r\,\mathrm{Re}\,\mathrm{Tr}\,U^r$ (and in models with pairing terms -- superconducting pairing -- additional $b_r\,\mathrm{Im}\,\mathrm{Tr}\,U^r$ terms appear). By invoking multivariate central limit theorems for vectors of traces of unitaries, we obtain a Gaussian distribution for $P(W)$ with variance $\mathrm{Var}(W)=\frac{1}{2}\sum_r r\,(a_r^2+b_r^2)$ and asymptotic independence across different powers. We also characterise the conditions under which non-Gaussian tails arise, for example from many interaction terms or their slow decay, as well as the appearance of Fisher--Hartwig singularities. We illustrate these mechanisms in the XY chain. Various numerical diagnostics support the analytical results.

quant-ph↗

arXiv2025

Analytical exploration of the optomechanical attractor diagram and of limit cycles

We analyse the interplay between mechanical and radiation pressure in an optomechanical cavity system. Our study is based on an analytical evaluation of the infinite Bessel summations involved, which previously had led to a numerical exploration of the so-called attractor diagram. The analytical expressions are then suitable for further asymptotic analysis in opposing regimes of the amplitude, which allows for a characterisation of the diagram in terms of elementary functions. Building on this framework, we investigate the emergence and properties of optomechanical limit cycles beyond the constraints of the resolved sideband approximation. By employing a Fokker-Planck formalism originally developed in the context of laser theory and then used in cavity optomechanics, we describe the quantum regime of these limit cycles, offering a more detailed and unified analytical perspective.

quant-ph↗

arXiv2025

Analytical control of the exchange interaction in periodically driven Mott insulators

The manipulation of electronic structure through periodic electric fields enables the reversible control of effective interactions in extended antiferromagnetic Mott insulators on ultrafast timescales. A careful analytical examination of the modulated effective interactions is conducted, accurately characterising it through the use of exact summation formulas and Bessel functions. As a result, time reversals are analytically determined in terms of Bessel zeroes. We discuss the half-filled Hubbard model, as well as multi-orbital models, various characteristics of the Kitaev-Heisenberg model, and the emergence of chiral spin terms.

cond-mat.str-el↗

arXiv2024

Hawking-Page transition on a spin chain

The accessibility of the Hawking-Page transition in AdS$_5$ through a 1d Heisenberg spin chain is demonstrated. We use the random matrix formulation of the Loschmidt echo for a set of spin chains, and randomize the ferromagnetic spin interaction. It is shown that the thermal Loschmidt echo, when averaged, detects the predicted increase in entropy across the Hawking-Page transition. This suggests that a 1d spin chain exhibits characteristics of black hole physics in 4+1 dimensions. We show that this approach is equally applicable to free fermion systems with a general dispersion relation.

quant-ph↗

arXiv2024

Dynamical quantum phase transitions from random matrix theory

We uncover a novel dynamical quantum phase transition, using random matrix theory and its associated notion of planar limit. We study it for the isotropic XY Heisenberg spin chain. For this, we probe its real-time dynamics through the Loschmidt echo. This leads to the study of a random matrix ensemble with a complex weight, whose analysis requires novel technical considerations, that we develop. We obtain three main results: 1) There is a third order phase transition at a rescaled critical time, that we determine. 2) The third order phase transition persists away from the thermodynamic limit. 3) For times below the critical value, the difference between the thermodynamic limit and a finite chain decreases exponentially with the system size. All these results depend in a rich manner on the parity of the number of flipped spins of the quantum state conforming the fidelity.

quant-ph↗

arXiv2024

Landau-Zener transition rates of superconducting qubits and absorption spectrum in quantum dots

New exact formulas are derived for systems involving Landau-Zener transition rates and for absorption spectra in quantum dots. These rectify previous inaccurate approximations utilized in experimental studies. The exact formulas give an explicit expression for the maxima and minima of the transition rate at any oscillating period and reveal a number of striking physical consequences, such as the suppression of oscillations for half-integer values of the detuning parameter and that the periodic dependence on the detuning parameter changes at special values of the driving field amplitude. The fluorescence spectra of quantum dots exhibit similar properties.

quant-ph↗

arXiv2022

Crystal bases and three-dimensional $ \mathcal{N}=4 $ Coulomb branches

We establish and develop a correspondence between certain crystal bases (Kashiwara crystals) and the Coulomb branch of three-dimensional $ \mathcal{N} =4 $ gauge theories. The result holds for simply-laced, non-simply laced and affine quivers. Two equivalent derivations are given in the non-simply laced case, either by application of the axiomatic rules or by folding a simply-laced quiver. We also study the effect of turning on real masses and the ensuing simplification of the crystal. We present a multitude of explicit examples of the equivalence. Finally, we put forward a correspondence between infinite crystals and Hilbert spaces of theories with isolated vacua.

hep-th↗

arXiv2022

Multiple phases and meromorphic deformations of unitary matrix models

We study a unitary matrix model with Gross-Witten-Wadia weight function and determinant insertions. After some exact evaluations, we characterize the intricate phase diagram. There are five possible phases: an ungapped phase, two different one-cut gapped phases and two other two-cut gapped phases. The transition from the ungapped phase to any gapped phase is third order, but the transition between any one-cut and any two-cut phase is second order. The physics of tunneling from a metastable vacuum to a stable one and of different releases of instantons is discussed. Wilson loops, $β$-functions and aspects of chiral symmetry breaking are investigated as well. Furthermore, we study in detail the meromorphic deformation of a general class of unitary matrix models, in which the integration contour is not anchored to the unit circle. The ensuing phase diagram is characterized by symplectic singularities and captured by a Hasse diagram.

hep-th↗