Wave packets from the spectrum

• URL: http://arxiv.org/abs/2606.10004v1
• Date: Mon, 08 Jun 2026 18:00:07 GMT
• Title: Wave packets from the spectrum
• Abstract summary: We show that any Hamiltonian can be made to look like such a theory.<n>We argue that our results are a step towards quantum mereology for fields.
• Score: 1.6528632644902823
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The freedom to change Fock basis seems to ensure a minimum amount of locality in lattice theories in the following sense: If $\lbrace (\hat a_i^\dagger\,,\,\hat a_i)\rbrace$ for $i=1,\dots,n$ is a lattice of creation and annihilation operators and if a given Hamiltonian $\hat H$ induces highly non-local dynamics on that lattice, then it will usually be possible to change to a new set of operators $\lbrace (\hat b_i^\dagger\,,\,\hat b_i)\rbrace$ in terms of which the dynamics appear less non-local. We demonstrate this by turning a highly non-local random matrix model into a local, 1D lattice theory where particles can propagate in localized wave packets. More generally, we show that any Hamiltonian can be made to look like such a theory, with the lattice dispersion relation and the non-integrability of the theory depending on the spectrum of $\hat H$. We argue that our results are a step towards quantum mereology for fields.

Related papers

• Nodal algebraic curves and entropy diagnostics in degenerate two-dimensional harmonic-oscillator shells [0.0]
  We show that degenerate quantum eigenspaces can support substantial changes in nodal geometry at fixed energy.<n>We combine these criteria with entropy diagnostics to identify strata where topology-changing events can occur.<n>The framework suggests experimentally reconstructible signatures for real-phase Hermite--Gaussian structured light and approximately isotropic trapped motional systems.
  arXiv  Detail & Related papers  (2026-04-30T17:15:26Z)
• Spectral statistics and energy-gap scaling in $k-$local spin Hamiltonians [0.0]
  We investigate the spectral properties of all-to-all interacting spin Hamiltonians acting on exactly $k$ spins.<n>For $mu = 0$, we demonstrate that the random matrix ensemble is determined by the parity of system size $L$ and locality $k$.<n>Our work introduces a semi-solvable model that captures universal features of random-matrix statistics, and spectral gap formation.
  arXiv  Detail & Related papers  (2025-10-17T17:11:38Z)
• Approximating the operator norm of local Hamiltonians via few quantum states [53.16156504455106]
  Consider a Hermitian operator $A$ acting on a complex Hilbert space of $2n$.<n>We show that when $A$ has small degree in the Pauli expansion, or in other words, $A$ is a local $n$-qubit Hamiltonian.<n>We show that whenever $A$ is $d$-local, textiti.e., $deg(A)le d$, we have the following discretization-type inequality.
  arXiv  Detail & Related papers  (2025-09-15T14:26:11Z)
• Monomer-dimer tensor-network basis for qubit-regularized lattice gauge theories [2.646330573001491]
  Traditional $mathrmSU(N)$ lattice gauge theories (LGTs) can be formulated using an orthonormal basis constructed from the irreducible representations (irreps) $V_lambda$ of the $mathrmSU(N)$ gauge symmetry.<n>Here, we investigate finite-temperature confinement-deconfinement transitions in a simple qubit-regularized $mathrmSU(2)$ and $mathrmSU(3)$ gauge theory.
  arXiv  Detail & Related papers  (2025-02-20T01:06:39Z)
• Quantum connection, charges and virtual particles [65.268245109828]
  A quantum bundle $L_hbar$ is endowed with a connection $A_hbar$ and its sections are standard wave functions $psi$ obeying the Schr"odinger equation. We will lift the bundles $L_Cpm$ and connection $A_hbar$ on them to the relativistic phase space $T*R3,1$ and couple them to the Dirac spinor bundle describing both particles and antiparticles.
  arXiv  Detail & Related papers  (2023-10-10T10:27:09Z)
• A Unified Framework for Uniform Signal Recovery in Nonlinear Generative Compressed Sensing [68.80803866919123]
  Under nonlinear measurements, most prior results are non-uniform, i.e., they hold with high probability for a fixed $mathbfx*$ rather than for all $mathbfx*$ simultaneously. Our framework accommodates GCS with 1-bit/uniformly quantized observations and single index models as canonical examples. We also develop a concentration inequality that produces tighter bounds for product processes whose index sets have low metric entropy.
  arXiv  Detail & Related papers  (2023-09-25T17:54:19Z)
• Systematics of quasi-Hermitian representations of non-Hermitian quantum models [0.0]
  This paper introduces and describes a set of constructive returns of the description to one of the correct and eligible physical Hilbert spaces $cal R_N(0)$. In the extreme of the theory the construction is currently well known and involves solely the inner product metric $Theta=Theta(H)$. At $j=N$ the inner-product metric remains trivial and only the Hamiltonian must be Hermitized, $H to mathfrakh = Omega,H,Omega-1=mathfrak
  arXiv  Detail & Related papers  (2022-12-07T20:10:58Z)
• Quantum double aspects of surface code models [77.34726150561087]
  We revisit the Kitaev model for fault tolerant quantum computing on a square lattice with underlying quantum double $D(G)$ symmetry. We show how our constructions generalise to $D(H)$ models based on a finite-dimensional Hopf algebra $H$.
  arXiv  Detail & Related papers  (2021-06-25T17:03:38Z)
• $T\ar T$-deformed Fermionic Theories Revisited [0.0]
  We revisit $Tbar T$ deformations of $d=2$ theories with fermions with a view toward the quantization. We ask about different $Tbar T$ deformations, such as manifestly supersymmetric $Tbar T$ and also more generally via the symmetric energy-momentum.
  arXiv  Detail & Related papers  (2021-04-19T18:00:07Z)
• Anharmonic oscillator: a solution [77.34726150561087]
  The dynamics in $x$-space and in $(gx)-space corresponds to the same energy spectrum with effective coupling constant $hbar g2$. A 2-classical generalization leads to a uniform approximation of the wavefunction in $x$-space with unprecedented accuracy.
  arXiv  Detail & Related papers  (2020-11-29T22:13:08Z)
• Floquet engineering of low-energy dispersions and dynamical localization in a periodically kicked three-band system [0.0]
  We numerically study the dynamics of a wave packet in dice lattice. We find a situation where absolute flat quasienergy bands lead to a complete dynamical localization of the wave packet.
  arXiv  Detail & Related papers  (2020-11-20T13:55:52Z)
• Emergent universality in critical quantum spin chains: entanglement Virasoro algebra [1.9336815376402714]
  Entanglement entropy and entanglement spectrum have been widely used to characterize quantum entanglement in extended many-body systems. We show that the Schmidt vectors $|v_alpharangle$ display an emergent universal structure, corresponding to a realization of the Virasoro algebra of a boundary CFT.
  arXiv  Detail & Related papers  (2020-09-23T21:22:51Z)
• Sub-bosonic (deformed) ladder operators [62.997667081978825]
  We present a class of deformed creation and annihilation operators that originates from a rigorous notion of fuzziness. This leads to deformed, sub-bosonic commutation relations inducing a simple algebraic structure with modified eigenenergies and Fock states. In addition, we investigate possible consequences of the introduced formalism in quantum field theories, as for instance, deviations from linearity in the dispersion relation for free quasibosons.
  arXiv  Detail & Related papers  (2020-09-10T20:53:58Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.