Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Zeitschrift für Physik A Hadrons and Nuclei

Lattice dynamics and transport equations for quantum crystals including singular interactions

H. Beck, P. F. Meier

Published Jun 1, 1971• 4 citations
Publisher
DOI
10.1007/bf01402489

Related papers

Transport theory for quantum crystals

W. Götze, K. H. Michel

Zeitschrift für Physik A Hadrons and Nuclei•Jun 1, 1969•29 citations

Expansion dynamics of strongly correlated lattice bosons: A self-consistent density-matrix approach

Julian Schwingel, Michael Turaev, Johann Kroha +1 more

We study the spatiotemporal dynamics of interacting bosons on a two-dimensional Hubbard lattice in the strongly interacting regime, taking into account the dynamics of condensate amplitude as well as the direct transport of noncondensed fluctuations. To that end we develop a self-consistent density-matrix approach which goes beyond the standard Gutzwiller mean-field theory. Starting from the Liouville-von-Neumann equation we derive a quantum master equation for the time evolution of the system's local density matrix at each lattice site, with a dynamical bath that represents the rest of the system. We apply this method to the expansion dynamics of an initially prepared cloud of interacting bosons in an optical lattice. We observe a ballistic expansion of the condensate, as expected, followed by slow, diffusive transport of the normal bosons. We discuss, in particular, the robustness of the Mott insulator phase as well as its melting due to incoherent transport. The method should be applicable to various models of lattice bosons in the strongly correlated regime.

arXiv:2507.09397•Physical Review A•Oct 1, 2025•0 citations

Quantum Lattice Model: Quantum Phase Transport and Wave Dynamics

Quinton R. D. Tharp

This paper develops the quantum dynamical layer of the Quantum Lattice Model (QLM) by showing how the standard wave equations of quantum mechanics arise as continuum descriptions of coherent phase-action transport on a discrete Planck-scale lattice. The framework is constructed from the per-radian Planck primitives {ℏ, ℓP, tP}, where each lattice tick advances physical phase by one radian and transports one quantum of reduced action. The corresponding phase-action and phase-flow relations are dS = ℏ dθ and E = ℏ dθ/dτ, while the invariant lattice transport identity c = ℓP/tP fixes the maximal causal phase-transport speed of the lattice. Starting from symmetric nearest-neighbor phase transport between Planck cells, the continuum limit yields the relativistic wave operator (1/c²)∂t² − ∇². Introducing intrinsic rest-phase rotation with frequency ω0 = mc²/ℏ produces the Klein-Gordon equation as the continuum description of synchronized spatial phase transport and local rest-phase rotation. A first-order relativistic factorization yields the Dirac equation, while extraction of the rapidly rotating rest-phase carrier produces the nonrelativistic Schrödinger equation governing slow envelope dynamics. Within this framework, the quantum wavefunction is interpreted as a coherent phase-envelope amplitude describing phase-action transport across the lattice. The conserved density ρ = |φ|² arises from the continuity equation of Schrödinger evolution, and the associated current takes the phase-flow form J = (ℏ/m)ρ∇θ. The paper also shows how interaction sectors enter the same transport framework as modular coupling layers. Scalar potentials contribute additional local phase rotation to the slow envelope, while routing-weighted transport modifies the effective capacity of lattice links. Coulomb coupling and weak-field gravitational coupling are presented as examples: the Coulomb potential appears as a scalar phase-rotation term, and gravitational routing modulation of the rest-phase carrier yields the weak-field potential V = mΦ. These results organize the Schrödinger, Klein-Gordon, and Dirac equations as successive continuum limits of deterministic phase-action transport on the Planck lattice, providing the quantum dynamical layer of the Quantum Lattice Model.

•Mar 8, 2026•0 citations

Lattice Dynamics of Quantum Crystals

T.R. KOEHLER

Methods in computational physics•Jan 1, 1976•6 citations

Anisotropic Quantum Emitter Interactions in Two-Dimensional Photonic-Crystal Baths

Alejandro González-Tudela, Fernando Galve

Quantum emitters interacting with two-dimensional photonic-crystal baths experience strong and anisotropic collective dissipation when they are spectrally tuned to 2D Van-Hove singularities. In this work, we show how to turn this dissipation into coherent dipole–dipole interactions with tunable range by breaking the lattice degeneracy at the Van-Hove point with a superlattice geometry. Using a coupled-mode description, we show that the origin of these interactions stems from the emergence of a qubit-photon bound state that inherits the anisotropic properties of the original dissipation and whose spatial decay can be tuned via the superlattice parameters or the detuning of the optical transition respect to the band-edges. Within that picture, we also calculate the emitter induced dynamics in an exact manner, bounding the parameter regimes where the dynamics lies within a Markovian description. As an application, we develop a four-qubit entanglement protocol exploiting the shape of the interactions. Finally, we provide a proof-of-principle example of a photonic crystal where such interactions can be obtained.

arXiv:1810.08155•ACS Photonics•Dec 20, 2018•32 citations

Thermodynamics and equations of motion of quantum crystals

Н. М. Лавріненко, S. V. Peletminskiǐ

Theoretical and Mathematical Physics•Feb 1, 1986•7 citations
We study the spatiotemporal dynamics of interacting bosons on a two-dimensional Hubbard lattice in the strongly interacting regime, taking into account the dynamics of condensate amplitude as well as the direct transport of noncondensed fluctuations. To that end we develop a self-consistent density-matrix approach which goes beyond the standard Gutzwiller mean-field theory. Starting from the Liouville-von-Neumann equation we derive a quantum master equation for the time evolution of the system's local density matrix at each lattice site, with a dynamical bath that represents the rest of the system. We apply this method to the expansion dynamics of an initially prepared cloud of interacting bosons in an optical lattice. We observe a ballistic expansion of the condensate, as expected, followed by slow, diffusive transport of the normal bosons. We discuss, in particular, the robustness of the Mott insulator phase as well as its melting due to incoherent transport. The method should be applicable to various models of lattice bosons in the strongly correlated regime.
This paper develops the quantum dynamical layer of the Quantum Lattice Model (QLM) by showing how the standard wave equations of quantum mechanics arise as continuum descriptions of coherent phase-action transport on a discrete Planck-scale lattice. The framework is constructed from the per-radian Planck primitives {ℏ, ℓP, tP}, where each lattice tick advances physical phase by one radian and transports one quantum of reduced action. The corresponding phase-action and phase-flow relations are dS = ℏ dθ and E = ℏ dθ/dτ, while the invariant lattice transport identity c = ℓP/tP fixes the maximal causal phase-transport speed of the lattice. Starting from symmetric nearest-neighbor phase transport between Planck cells, the continuum limit yields the relativistic wave operator (1/c²)∂t² − ∇². Introducing intrinsic rest-phase rotation with frequency ω0 = mc²/ℏ produces the Klein-Gordon equation as the continuum description of synchronized spatial phase transport and local rest-phase rotation. A first-order relativistic factorization yields the Dirac equation, while extraction of the rapidly rotating rest-phase carrier produces the nonrelativistic Schrödinger equation governing slow envelope dynamics. Within this framework, the quantum wavefunction is interpreted as a coherent phase-envelope amplitude describing phase-action transport across the lattice. The conserved density ρ = |φ|² arises from the continuity equation of Schrödinger evolution, and the associated current takes the phase-flow form J = (ℏ/m)ρ∇θ. The paper also shows how interaction sectors enter the same transport framework as modular coupling layers. Scalar potentials contribute additional local phase rotation to the slow envelope, while routing-weighted transport modifies the effective capacity of lattice links. Coulomb coupling and weak-field gravitational coupling are presented as examples: the Coulomb potential appears as a scalar phase-rotation term, and gravitational routing modulation of the rest-phase carrier yields the weak-field potential V = mΦ. These results organize the Schrödinger, Klein-Gordon, and Dirac equations as successive continuum limits of deterministic phase-action transport on the Planck lattice, providing the quantum dynamical layer of the Quantum Lattice Model.
Quantum emitters interacting with two-dimensional photonic-crystal baths experience strong and anisotropic collective dissipation when they are spectrally tuned to 2D Van-Hove singularities. In this work, we show how to turn this dissipation into coherent dipole–dipole interactions with tunable range by breaking the lattice degeneracy at the Van-Hove point with a superlattice geometry. Using a coupled-mode description, we show that the origin of these interactions stems from the emergence of a qubit-photon bound state that inherits the anisotropic properties of the original dissipation and whose spatial decay can be tuned via the superlattice parameters or the detuning of the optical transition respect to the band-edges. Within that picture, we also calculate the emitter induced dynamics in an exact manner, bounding the parameter regimes where the dynamics lies within a Markovian description. As an application, we develop a four-qubit entanglement protocol exploiting the shape of the interactions. Finally, we provide a proof-of-principle example of a photonic crystal where such interactions can be obtained.