arXiv subjects

Friedrich Hübner

Publications and source records attributed to Friedrich Hübner.

18 recordsLinked to original sources

arXiv2026

Solvable relaxation in discrete unitary systems: Ruelle-Pollicott resonances and CMV matrices

Leading eigenvalues of the truncated propagator, known as Ruelle-Pollicott (RP) resonances, are an elegant way of addressing the dynamics of unitary many-body systems. We study unitary propagators in their canonical form, known in the mathematical literature as the CMV matrices, and obtain a number of exact results for RP resonances and the associated norm-diverging eigenvectors. For the simplest CMV class describing a unilateral shift with an impurity, motivated by operator dynamics in dual-unitary circuits, we obtain closed-form results and in particular show that the three independent ways of obtaining RP resonances -- the truncated propagator, analytic continuation of the resolvent, and the rigged Hilbert space approach -- all give the same results. In more realistic CMV matrices, in which shift-like operator dynamics characteristic of chaotic systems is only asymptotic, we rely on the rich theory of orthogonal polynomials on the unit circle and identify two phases. In the first phase, relaxation occurs due to local operators effectively evolving into increasingly nonlocal ones with negligible backflow. Especially interesting is the second phase, which, surprisingly, exhibits faster relaxation because of contributions from the backflow of large operators. Additionally, in the second phase, RP resonances are not equal to the eigenvalues of the truncated propagator, instead, they are ``hidden'' within a ring of ill-conditioned eigenvalues.

cond-mat.stat-mech↗

arXiv2026

Interacting Quantum Symmetric Exclusion Process

We introduce and solve the Interacting Quantum Symmetric Exclusion Process (IQSEP), a family of models describing the stochastic quantum hopping of charged particles along the edges of a lattice, with hopping amplitudes that depend on the occupations of neighbouring sites. In the absence of interactions, they reduce to the standard quantum simple symmetric exclusion process, exhibiting coherent diffusive transport. For interactions of order one, they capture incoherent diffusive transport and its fluctuations, characterized by density-dependent diffusivity and mobility, making contact with the macroscopic fluctuation theory. By rescaling the interaction strength appropriately with the lattice mesh, we define a mesoscopic scaling regime that retains a finite coherence length in the continuous thermodynamic limit. This regime interpolates between coherent behavior at small length scales and incoherent behavior at large scales. The resulting scaling theory accounts for fluctuations of quantum coherences in interacting diffusive systems, going beyond the scope of standard fluctuating hydrodynamics.

cond-mat.stat-mech↗

arXiv2026

Influence-solvability: a systematic theory of $(1+1)D$ solvability and its application to brickwork circuits

`Solvable' circuits, such as dual unitaries and its generalisations, have arisen as paradigmatic examples of tractable chaotic non-equilibrium dynamics, both in classical and quantum systems. However, while increasingly more complicated sufficient conditions have been proposed, a systematic theory classifying and understanding general features of solvable circuits is missing. We develop such a theory by introducing influence-solvable circuits, a class of $(1+1)D$ circuits whose influence matrix, which represents the `bath' generated by its own evolution, is given by a uniform MPS with finite bond-dimension $χ$. This property allows for efficient computation of subsystem dynamics and essentially contains all known examples of solvable circuits. We derive a set of necessary and sufficient local conditions by using a version of the fundamental theorem of MPS for open boundary conditions. Next we apply our theory to brickwork circuits with $χ=1$ influence-solvability and perform a systematic classification of classical brickwork circuits with local dimension up to $d=3$ and quantum brickwork circuits with $d=2$. Our search reveals new solvable circuits that are not captured by known solvability conditions.

cond-mat.stat-mech↗

arXiv2026

Towards an ab initio derivation of generalised hydrodynamics from a gas of interacting wave packets

We present steps towards an ab initio derivation of generalised hydrodynamics in quantum integrable models, starting from the Bethe wave functions, and explained on the example of the repulsive Lieb-Liniger model. This includes an identification of the generalised hydrodynamics quasi-particles as wave packets in the quantum model. These wave packets evolve according to a classical particle model and collect two-particle scattering shifts similar to solitons in integrable PDEs. We then discuss potential routes to obtain the generalised hydrodynamics equation for average conserved densities in long-wavelength states from this description. As part of this, we provide an explicit formula for the action of the spectral phase-space density operator on Bethe wave functions, and show that it generates local conserved densities.

cond-mat.stat-mech↗

arXiv2025

Diffusive hydrodynamics from long-range correlations

In the hydrodynamic theory, the non-equilibrium dynamics of a many-body system is approximated, at large scales of space and time, by irreversible relaxation to local entropy maximisation. This results in a convective equation corrected by viscous or diffusive terms in a gradient expansion, such as the Navier-Stokes equations. Diffusive terms are evaluated using the Kubo formula, and possibly arising from an emergent noise due to discarded microscopic degrees of freedom. In one dimension of space, diffusive scaling is often broken as noise leads to super-diffusion. But in linearly degenerate hydrodynamics, such as that of integrable models, diffusive behaviors are observed, and it has long be thought that the standard diffusive picture remains valid. In this letter, we show that in such systems, the Navier-Stokes equation breaks down beyond linear response. We demonstrate that diffusive-order corrections do not take the form of a gradient expansion. Instead, they are completely determined by ballistic transport of initial-state fluctuations, and obtained from the non-local two-point correlations recently predicted by the ballistic macroscopic fluctuation theory (BMFT); the resulting hydrodynamic equations are reversible. To do so, we establish a regularised fluctuation theory, putting on a firm basis the recent idea that ballistic transport of initial-state fluctuations determines fluctuations and correlations beyond the Euler scale. This extends the idea of ``diffusion from convection'' previously developed to explain the Kubo formula in integrable systems, to generic non-equilibrium settings.

cond-mat.stat-mech↗

arXiv2025

On the Hydrodynamic Approximation of Quantum Integrable Models -- An Illustration via the repulsive Lieb-Liniger Model

Generalized hydrodynamics is a framework to study the large scale dynamics of integrable models, special fine-tuned one-dimensional many-body systems that possess an infinite number of local conserved quantities. Unlike classical models, where the microscopic origins of generalized hydrodynamics are better understood, in quantum models it can only be derived using the hydrodynamic formalism. Using the paradigmatic and experimentally relevant repulsive Lieb-Liniger model as an example, this thesis introduces a new viewpoint on the dynamics of quantum integrable models by introducing so-called semi-classical Bethe models. These classical integrable models act as an intermediate description between the microscopic quantum realm and the macroscopic generalized hydrodynamics. After introducing these models and discussing their properties, we study the generalized hydrodynamics equation using new tools and show that solutions to the Euler generalized hydrodynamics equation of the Lieb-Liniger model exist, are unique and do not develop gradient catastrophes. Finally, we discuss new insights into the physics governing the diffusive correction, which, contrary to prior belief, is not described by a Navier-Stokes-like equation. Focusing on the main intuitive ideas, the thesis aims to provide a self-contained overview over these exciting new developments on generalized hydrodynamics.

cond-mat.stat-mech↗

arXiv2025

Hydrodynamics without Averaging -- a Hard Rods Study

On the example of the integrable hard rods model we study the quality of the (generalized) hydrodynamic approximation on a single coarse-grained sample. This is opposed to the traditional approach which averages over an appropriate local equilibrium state. While mathematically more ambiguous, a major advantage of the new approach is that it allows us to disentangle intrinsic diffusion from `diffusion from convection' effects. For the hard rods we find intrinsic diffusion is absent, which agrees with and clarifies recent findings. Interestingly, the results also apply to not locally thermal states, demonstrating that hydrodynamics (in this model) does not require the assumption of local equilibrium.

cond-mat.stat-mech↗

arXiv2025

A new quadrature for the generalized hydrodynamics equation and absence of shocks in the Lieb-Liniger model

In conventional fluids, it is well known that Euler-scale equations are plagued by ambiguities and instabilities. Smooth initial conditions may develop shocks, and weak solutions, such as for domain wall initial conditions (the paradigmatic Riemann problem of hydrodynamics), are not unique. The absence of shock formation experimentally observed in quasi-one-dimensional cold-atomic gases, which are described by the Lieb-Liniger model, provides perhaps the strongest pointer to a modification of the hydrodynamic equation due to integrability. Generalised hydrodynamics (GHD) is the required hydrodynamic theory, taking into account the infinite number of conserved quantities afforded by integrability. We provide a new quadrature for the GHD equation -- a solution in terms of a Banach fixed-point problem where time has been explicitly integrated. The quadrature is an efficient numerical solution tool; and it allows us, in the Lieb-Liniger model, to rigorously show that no shock may appear at all times, and, when combined with recent hydrodynamic fluctuation theories, to obtain new expressions for correlations in non-stationary states, establishing for the first time the presence of discontinuities characteristic of the non-equilibrium dynamics.

cond-mat.stat-mech↗

arXiv2025

Diffusive hydrodynamics of hard rods from microscopics

We derive exact equations governing the large-scale dynamics of hard rods, including diffusive effects that go beyond ballistic transport. Diffusive corrections are the first-order terms in the hydrodynamic gradient expansion and we obtain them through an explicit microscopic calculation of the dynamics of hard rods. We show that they differ significantly from the prediction of Navier-Stokes hydrodynamics, as the correct hydrodynamics description is instead given by two coupled equations, giving respectively the evolution of the one point functions and of the connected two-point correlations. The resulting equations are time-reversible and reduce to the usual Navier-Stokes hydrodynamic equations in the limit of near-equilibrium evolution. This represents the first exact microscopic calculation showing how ballistic dynamics generates long-range correlations, in agreement with general results from the recently developed ballistic macroscopic fluctuation theory, and showing how such long range-correlations directly affect the diffusive hydrodynamic terms, in agreement with, and clarifying, recent related results.

cond-mat.stat-mech↗

arXiv2025

Generalized hydrodynamics of integrable quantum circuits

Quantum circuits make it possible to simulate the continuous-time dynamics of a many-body Hamiltonian by implementing discrete Trotter steps of duration $τ$. However, when $τ$ is sufficiently large, the discrete dynamics exhibit qualitative differences compared to the original evolution, potentially displaying novel features and many-body effects. We study an interesting example of this phenomenon, by considering the integrable Trotterization of a prototypical integrable model, the XXZ Heisenberg spin chain. We focus on the well-known bipartition protocol, where two halves of a large system are prepared in different macrostates and suddenly joined together, yielding non-trivial nonequilibrium dynamics. Building upon recent results and adapting the generalized hydrodynamics (GHD) of integrable models, we develop an exact large-scale description of an explicit one-dimensional quantum-circuit setting, where the input left and right qubits are initialized in two distinct product states. We explore the phenomenology predicted by the GHD equations, which depend on the Trotter step and the gate parameters. In some phases of the parameter space, we show that the quantum-circuit large-scale dynamics is qualitatively different compared to the continuous-time evolution. In particular, we find that a single microscopic defect at the junction, such as the addition of a single qubit, may change the nonequilibrium macrostate appearing at late time.

cond-mat.stat-mech↗

arXiv2025

Circuits as a simple platform for the emergence of hydrodynamics in deterministic chaotic many-body systems

The emergence of hydrodynamics is one of the deepest phenomena in many-body systems. Arguably, the hydrodynamic equations are also the most important tools for predicting large-scale behaviour. Understanding how such equations emerge from microscopic deterministic dynamics is a century-old problem, despite recent progress in fine-tuned integrable systems. Due to the universality of hydrodynamics, the specific microscopic implementation should not matter. Here, we show that classical deterministic circuits provide a minimal, exact, and efficient platform that admits non-trivial hydrodynamic behaviour for deterministic but chaotic systems. By developing new techniques and focusing on 1D circuits as a proof of concept, we obtain the characteristic dynamics, including relaxation to Gibbs states, exact Euler equations, shocks, diffusion, and exact KPZ super-diffusion. Our methods can be easily generalised to higher dimensions or quantum circuits.

cond-mat.stat-mech↗

arXiv2024

Existence and Uniqueness of Solutions to the Generalized Hydrodynamics Equation

The generalized hydrodynamics (GHD) equation is the equivalent of the Euler equations of hydrodynamics for integrable models. Systems of hyperbolic equations such as the Euler equations usually develop shocks and are plagued by problems of uniqueness. We establish for the first time the existence and uniqueness of solutions to the full GHD equation and the absence of shocks, from a large class of initial conditions with bounded occupation function. We assume only absolute integrability of the two-body scattering shift. In applications to quantum models of fermionic type, this includes all commonly used physical initial states, such as locally thermal states and zero-entropy states. We show in particular that differentiable initial conditions give differentiable solutions at all times and that weak initial conditions such as the Riemann problem have unique weak solutions which preserve entropy. For this purpose, we write the GHD equation as a new fixed-point problem (announced in a companion paper). We show that the fixed point exists, is unique, and is approached, under an iterative solution procedure, in the Banach topology on functions of momenta.

math-ph↗

arXiv2024

Mesoscopic Impurities in Generalized Hydrodynamics

We study impurities in integrable models from the viewpoint of generalized hydrodynamics (GHD). An impurity can be thought of as a boundary condition for the GHD equation, relating the state on the left and right side. We find that in interacting models it is not possible to disentangle incoming and outgoing states, which means that it is not possible to think of scattering as a mapping which maps the incoming state to the outgoing state. We then introduce a novel class of impurities, dubbed mesoscopic impurities, whose spatial size is mesoscopic (i.e.\ their size $L_{\mathrm{micro}} \ll L_{\mathrm{imp}} \ll L$ is much larger than the microscopic length scale $L_{\mathrm{micro}}$, but much smaller than the macroscopic scale $L$). Due to their large size it is possible to describe mesoscopic impurities via GHD. This simplification allows one to study these impurities both analytically and numerically. These impurities show interesting non-perturbative scattering behavior, for instance non-uniqueness of solutions and a non-analytic dependence on the impurity strength. In models with one quasi-particle species and a scattering phase shift that depends on the difference of momenta only, we find that one can describe the scattering using an effective Hamiltonian. This Hamiltonian is dressed due to the interaction between particles and satisfies a self consistency fixed point equation. On the example of the hard rods model we demonstrate how this fixed point equation can be used to find almost explicit solutions to the scattering problem by reducing it to a two-dimensional system of equations which can be solved numerically.

cond-mat.stat-mech↗

arXiv2024

New classical integrable systems from generalized $T\bar{T}$-deformations

We introduce and study a novel class of classical integrable many-body systems obtained by generalized $T\bar{T}$-deformations of free particles. Deformation terms are bilinears in densities and currents for the continuum of charges counting asymptotic particles of different momenta. In these models, which we dub ``semiclassical Bethe systems'' for their link with the dynamics of Bethe ansatz wave packets, many-body scattering processes are factorised, and two-body scattering shifts can be set to an almost arbitrary function of momenta. The dynamics is local but inherently different from that of known classical integrable systems. At short scales, the geometry of the deformation is dynamically resolved: either particles are slowed down (more space available), or accelerated via a novel classical particle-pair creation/annihilation process (less space available). The thermodynamics both at finite and infinite volumes is described by the equations of (or akin to) the thermodynamic Bethe ansatz, and at large scales generalized hydrodynamics emerge.

cond-mat.stat-mech↗

arXiv2023

Generalised $T\bar{T}$-deformations of classical free particles

Deformations of many-body Hamiltonians by certain products of conserved currents, referred to as $T\bar{T}$-deformations, are known to preserve integrability. Generalised $T\bar{T}$-deformations, based on the complete space of pseudolocal currents, were suggested [B. Doyon, J, Durnin, T. Yoshimura, Scipost Physics 13, 072 (2022)] to give rise to integrable systems with arbitrary two-body scattering shifts, going beyond those from known models or standard CDD factors. However, locality properties were not clear. We construct explicit generalised $T\bar{T}$-deformations of the system of classical free particles. We show rigorously that they are Liouville integrable Hamiltonian systems with finite-range interactions. We show elastic, factorised scattering, with a two-particle scattering shift that can be any continuously differentiable non-negative even function of momentum differences, fixed by the $T\bar{T}$-deformation function. We show that the scattering map (or wave operator) has a finite-range property allowing us to trace carriers of asymptotic momenta even at finite times - an important characteristics of many-body integrability. We evaluate the free energy and prove the thermodynamic Bethe ansatz with Maxwell-Boltzmann statistics, including with space-varying potentials and in finite and infinite volumes. We give equations for the particles' trajectories where time appears explicitly, generalising the contraction map of hard rod systems: the effect of generalised $T\bar{T}$-deformations is to modify the local metric perceived by each particle, adding extra space in a way that depends on their neighbours. The systems generalise the gas of interacting Bethe ansatz wave packets recently introduced in the Lieb-Liniger model. They form a new class of models that, we believe, most clearly make manifest the structures of many-body integrability.

cond-mat.stat-mech↗

arXiv2023

Suppression of scattering from slow to fast subsystems and application to resonantly Floquet-driven impurities in strongly interacting systems

We study solutions to the Lippmann-Schwinger equation in systems where a slow subsystem is coupled to a fast subsystem via an impurity. Such situations appear when a high-frequency Floquet-driven impurity is introduced into a low-energy system, but the driving frequency is at resonance with a high-energy band. In contrast to the case of resonant bulk driving, where the particles in the low-energy system are excited into the high-energy band, we surprisingly find that these excitations are suppressed for resonantly driven impurities. Still, the transmission through the impurity is strongly affected by the presence of the high-energy band in a universal way that does not depend on the details of the high-energy band. We apply our general result to two examples and show the suppression of excitations from the low-energy band into the high-energy band: a) bound pairs in a Fermi-Hubbard chain scattering at a driven impurity, which is at resonance with the Hubbard interaction and b) particles in a deep optical lattice described by the tight-binding approximation, which scatter at a driven impurity, whose driving frequency equals the band gap between the two lowest energy bands.

cond-mat.stat-mech↗

arXiv2023

Momentum resolved Floquet-engineered pair and single particle filter in the Fermi Hubbard model

We investigate the transport properties of a Fermi-Hubbard chain with an impurity which is formed by a site with a periodically modulated chemical potential. We determine the momentum resolved transmission through this impurity in dependence of the modulation frequency and strength for a single particle and a pair of fermions. We find that the pair transmission has a very distinct behaviour from the single particle transmission. Different situations can occur, where only the single particle or the pair with a certain momentum are transmitted or filtered out.

cond-mat.quant-gas↗

arXiv2021

Floquet-engineered pair and single particle filter in the Fermi Hubbard model

We investigate the Fermi-Hubbard model with a Floquet-driven impurity in the form of a local time-oscillating potential. For strong attractive interactions a stable formation of pairs is observed. These pairs show a completely different transmission behavior than the transmission that is observed for the single unpaired particles. Whereas in the high frequency limit the single particles show a maximum of the transition at low driving amplitudes, the pairs display a pronounced maximum transmission when the amplitude of the driving lies close to the ratio of the interaction U and the driving frequency ω. We use the distinct transmission behaviour to design filters for pairs or single particles, respectively. For example one can totally block the transmission of single particles through the driven impurity and allow only for the transmission of pairs. We quantify the quality of the designed filters.

cond-mat.quant-gas↗