Per Moosavi

Last Name

Moosavi

First Name

Per

ORCID

0000-0003-0011-2937

Organisational unit

03355 - Graf, Gian Michele / Graf, Gian Michele

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Publications 1 - 9 of 9

Exact Dirac–Bogoliubov–de Gennes Dynamics for Inhomogeneous Quantum Liquids
Moosavi, Per (2023)
Physical Review Letters
We study inhomogeneous 1+1-dimensional quantum many-body systems described by Tomonaga-Luttinger-liquid theory with general propagation velocity and Luttinger parameter varying smoothly in space, equivalent to an inhomogeneous compactification radius for free boson conformal field theory. This model appears prominently in low-energy descriptions, including for trapped ultracold atoms, while here we present an application to quantum Hall edges with inhomogeneous interactions. The dynamics is shown to be governed by a pair of coupled continuity equations identical to inhomogeneous Dirac-Bogoliubov-de Gennes equations with a local gap and solved by analytical means. We obtain their exact Green's functions and scattering matrix using a Magnus expansion, which generalize previous results for conformal interfaces and quantum wires coupled to leads. Our results explicitly describe the late-time evolution following quantum quenches, including inhomogeneous interaction quenches, and Andreev reflections between coupled quantum Hall edges, revealing remarkably universal dependence on details at stationarity or at late times out of equilibrium.
Breaking of Huygens-Fresnel principle in inhomogeneous Tomonaga-Luttinger liquids
Gluza, Marek; Moosavi, Per; Sotiriadis, Spyros (2022)
Journal of Physics A: Mathematical and Theoretical
Tomonaga-Luttinger liquids (TLLs) can be used to effectively describe one-dimensional quantum many-body systems such as ultracold atoms, charges in nanowires, superconducting circuits, and gapless spin chains. Their properties are given by two parameters, the propagation velocity and the Luttinger parameter. Here we study inhomogeneous TLLs where these are promoted to functions of position and demonstrate that they profoundly affect the dynamics: in general, besides curving the light cone, we show that propagation is no longer ballistically localized to the light-cone trajectories, different from standard homogeneous TLLs. Specifically, if the Luttinger parameter depends on position, the dynamics features pronounced spreading into the light cone, which cannot be understood via a simple superposition of waves as in the Huygens-Fresnel principle. This is the case for ultracold atoms in a parabolic trap, which serves as our main motivation, and we discuss possible experimental observations in such systems.
Geometric approach to inhomogeneous Floquet systems
Lapierre, Bastien; Moosavi, Per (2021)
Physical Review B
We present a new geometric approach to Floquet many-body systems described by inhomogeneous conformal field theory in 1+1 dimensions. It is based on an exact correspondence with dynamical systems on the circle that we establish and use to prove existence of (non)heating phases characterized by the (absence) presence of fixed or higher-periodic points of coordinate transformations encoding the time evolution: Heating corresponds to energy and excitations concentrating exponentially fast at unstable such points while nonheating to pseudoperiodic motion. We show that the heating rate (serving as the order parameter for transitions between these two) can have cusps, even within the overall heating phase, and that there is a rich structure of phase diagrams with different heating phases distinguishable through kinks in the entanglement entropy, reminiscent of Lifshitz phase transitions. Our geometric approach generalizes previous results for a subfamily of similar systems that used only the sl(2) algebra to general smooth deformations that require the full infinite-dimensional Virasoro algebra, and we argue that it has wider applicability, even beyond conformal field theory. ©2021 American Physical Society
Inhomogeneous Conformal Field Theory Out of Equilibrium
Moosavi, Per (2024)
Annales Henri Poincaré
We study the non-equilibrium dynamics of conformal field theory (CFT) in 1+1 dimensions with a smooth position-dependent velocity v(x) explicitly breaking translation invariance. Such inhomogeneous CFT is argued to effectively describe 1+1-dimensional quantum many-body systems with certain inhomogeneities varying on mesoscopic scales. Both heat and charge transport are studied, where, for concreteness, we suppose that our CFT has a conserved U(1) current. Based on projective unitary representations of diffeomorphisms and smooth maps in Minkowskian CFT, we obtain a recipe for computing the exact non-equilibrium dynamics in inhomogeneous CFT when evolving from initial states defined by smooth inverse-temperature and chemical-potential profiles β(x) and μ(x). Using this recipe, the following exact analytical results are obtained: (i) the full time evolution of densities and currents for heat and charge transport, (ii) correlation functions for components of the energy–momentum tensor and the U(1) current as well as for any primary field, and (iii) the thermal and electrical conductivities. The latter are computed by direct dynamical considerations and alternatively using a Green–Kubo formula. Both give the same explicit expressions for the conductivities, which reveal how inhomogeneous dynamics opens up the possibility for diffusion as well as implies a generalization of the Wiedemann–Franz law to finite times within CFT.
Approaching off-diagonal long-range order for 1+1-dimensional relativistic anyons
Fresta, Luca; Moosavi, Per (2021)
Physical Review B
We construct and study relativistic anyons in 1+1 dimensions generalizing well-known models of Dirac fermions. First, a model of free anyons is constructed and then extended in two ways: (i) by adding density-density interactions, as in the Luttinger model, and (ii) by coupling the free anyons to a U(1)-gauge field, as in the Schwinger model. Second, physical properties of these extensions are studied. By investigating off-diagonal long-range order (ODLRO) at zero temperature, we show that anyonic statistics allows one to get arbitrarily close to ODLRO but that this possibility is destroyed by the gauge coupling. The latter is due to a nonzero effective mass generated by gauge invariance, which we show also implies the presence of screening, independently of the anyonic statistics. © 2021 American Physical Society
Stability of the Classical Catenoid and Darboux–Pöschl–Teller Potentials
Hoppe, Jens; Moosavi, Per (2022)
Mathematical Physics, Analysis and Geometry
We revisit the stability (instability) of the outer (inner) catenoid connecting two concentric circular rings and give an explicit new construction of the unstable mode of the inner catenoid by studying the spectrum of an exactly solvable one-dimensional Schrödinger operator with an asymmetric Darboux–Pöschl–Teller potential.
Emergence of generalized hydrodynamics in the non-local Luttinger model
Moosavi, Per (2020)
SciPost Physics
We propose the Luttinger model with finite-range interactions as a simple tractable example in 1+1 dimensions to analytically study the emergence of Euler-scale hydrodynamics in a quantum many-body system. This non-local Luttinger model is an exactly solvable quantum field theory somewhere between conformal and Bethe-ansatz integrable models. Applying the recent proposal of generalized hydrodynamics, we show that the model allows for fully explicit yet non-trivial solutions of the resulting Euler-scale hydrodynamic equations. Comparing with exact analytical non-equilibrium results valid at all time and length scales, we show perfect agreement at the Euler scale when the interactions are short range. A formal proof of the emergence of generalized hydrodynamics in the non-local Luttinger model is also given, and effects of long-range interactions are briefly discussed.
Anisotropic Quantum Hall Droplets
Oblak, Blagoje; Lapierre, Bastien; Moosavi, Per; et al. (2024)
Physical Review X
We study two-dimensional (2D) droplets of noninteracting electrons in a strong magnetic field, placed in a confining potential with arbitrary shape. Using semiclassical methods adapted to the lowest Landau level, we obtain near-Gaussian energy eigenstates that are localized on level curves of the potential and have a position-dependent height. This one-particle insight allows us to deduce explicit formulas for expectation values of local many-body observables, such as density and current, in the thermodynamic limit. In particular, correlations along the edge are long-ranged and inhomogeneous. As we show, this is consistent with the system's universal low-energy description as a free 1D chiral conformal field theory of edge modes, known from earlier works in simple geometries. A delicate interplay between radial and angular dependencies of eigenfunctions ultimately ensures that the theory is homogeneous in terms of the canonical angle variable of the potential, despite its apparent inhomogeneity in terms of more naïve angular coordinates. Finally, we propose a scheme to measure the anisotropy by subjecting the droplet to microwave radiation; we compute the corresponding absorption rate and show that it depends on the droplet's shape and the waves' polarization. These results, both local and global, are likely to be observable in solid-state systems or quantum simulators of 2D electron gases with a high degree of control on the confining potential.
Marginal quenches and drives in Tomonaga-Luttinger liquids
Datta, Shouvik; Lapierre, Bastien; Moosavi, Per; et al. (2023)
SciPost Physics
We study Tomonaga-Luttinger liquids thrown out of equilibrium by marginal deformations in the form of interaction modulations. This is modeled by quenching or periodically driving the Luttinger parameter or, equivalently, the compactification radius of the free boson conformal field theory between two different values. We obtain exact analytical results for the evolution of the Loschmidt echo and observables such as the particle and energy densities. Starting from generic initial states, the quench dynamics are shown to exhibit revivals and temporal orthogonalities. For the periodic drive, we show stability or instability of time-evolved physical quantities dependent on the drive parameters. We also compare the corresponding marginally deformed thermal density matrices by non-perturbatively evaluating their Rényi divergence as a Euclidean quench. All the dynamics are shown to be crucially dependent on the ratio of the Luttinger parameters, which corresponds to the Zamolodchikov distance in the space of marginal deformations. Our setup is equivalently interpreted as the dynamics of the bosonic string upon instantaneous changes of the target-space radius.

Publications 1 - 9 of 9

Per Moosavi

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