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

arXiv:0709.2526 · Physical Review Letters

Many Body Generalization of the Landau-Zener Problem

Alexander Altland, Victor Gurarie

Published Feb 15, 2008• 65 citations
arXivHTMLPDF

Abstract

We formulate and approximately solve a specific many body generalization of the Landau-Zener problem. Unlike with the single particle Landau-Zener problem, our system does not abide in the adiabatic ground state, even at very slow driving rates. The structure of the theory suggests that this finding reflects a more general phenomenon in the physics of adiabatically driven many particle systems. Our solution can be used to understand, for example, the behavior of two-level systems coupled to an electromagnetic field, as realized in cavity QED experiments.

DOI
10.1103/physrevlett.100.063602

Related papers

Nonadiabaticity and large fluctuations in a many-particle Landau-Zener problem

Alexander Altland, Victor Gurarie, Thomas Kriecherbauer +1 more

We consider the behavior of an interacting many-particle system under slow external driving---a many-body generalization of the Landau-Zener paradigm. We find that a conspiracy of interactions and driving leads to physics profoundly different from that of the single-particle limit: for practically all values of the driving rate the particle distributions in Hilbert space are very broad, a phenomenon caused by a strong amplification of quantum fluctuations in the driving process. These fluctuations are ``nonadiabatic'' in that even at very slow driving it is exceedingly difficult to push the center of the distribution toward the limit of full ground-state occupancy. We obtain these results by a number of complementary theoretical approaches, including diagrammatic perturbation theory, semiclassical analysis, and exact diagonalization.

arXiv:0811.2527•Physical Review A•Apr 2, 2009•90 citations

Unconventional Landau-Zener type transitions in many-body systems

Jonas Larson

Institut fu¨r Theoretische Physik, Universita¨t zu K¨oln, De-50937 K¨oln, Germany(Dated: December 16, 2013)Landau-Zener transitions in a Lipkin-Meshkov-Glick model are considered, both as a single systemand in a lattice where each individual site hosts a realization of the corresponding many-bodyproblem. The single site mean-field problem is conceptually different from many other non-linearLandau-Zener models - it does not support any hysteresis and a new phenomenon appears whereadiabaticity totaly breaks down. More precisely, thisbreakdown occurs for isolated classical solutionspropagating on a separatrix in phase space and during the Landau-Zener sweep they get locked toa fixed point which prohibits adiabatic following. Quantum fluctuations tend to destabilize thesesolutions such that for moderate particle numbers the phenomenon is lost. At the quantum levelit is also shown that the non-adiabatic corrections P of the single site problem obey a power-lawdependenceon the Landau-Zenersweep velocity λ in the adiabatic regime, i.e. P ∼ λ

•Oct 29, 2013•0 citations

Phase diagram of Landau-Zener phenomena in coupled one-dimensional Bose quantum fluids

Santiago F. Caballero-Benítez, R. Paredes

We study stationary and dynamical properties of the many-body Landau-Zener dynamics of a Bose quantum fluid confined in two coupled one-dimensional chains by using a many-body generalization recently reported Chen et al. [Nature Phys. 7, 61 (2011)], within the decoupling approximation and the one-level band scheme. The energy spectrum shows evidence of the structure of the avoided level crossings as a function of the onsite interparticle interaction strength. On the dynamical side, a phase diagram of the transfer efficiency across ground-state and inverse sweeps is presented. A totally different scenario with respect to the original single-particle Landau-Zener scheme is found for ground-state sweeps, in which a breakdown of the adiabatic region emerges as the sweep rate decreases. On the contrary, the transfer efficiency across inverse sweeps reveals consistent results with the single-particle Landau-Zener predictions. In the strong-coupling regime, we find that there is a critical value of the onsite interaction for which the transfer of particles starts to vanish independently of the sweep rate. Our results are in qualitative agreement with those of the experimental counterpart.

arXiv:1106.6179•Physical Review A•Feb 6, 2012•17 citations

Generalizations of the Landau-Zener theory in the physics of nanoscale systems

Nikolai A. Sinitsyn

Nanoscale systems have sizes intermediate between atomic and macroscopic ones. Therefore their treatment often requires a combination of methods from atomic and condensed matter physics. The conventional Landau-Zener theory, being a powerful tool in atomic physics, often fails to predict correctly nonadiabatic transition probabilities in various nanostructures because it does not include many-body effects typical for mesoscopics. In this research project the generalizations of the Landau-Zener theory that solve this problem were studied. The multistate, multiparticle and nonunitary extensions of the theory have been proposed and investigated. New classes of exactly solvable models have been derived. I discuss their applications in problems of the molecular condensate dissociation and of the driven charge transport. In application to the physics of nanomagnets new approaches in modeling the influence of the environment on the Landau-Zener evolution are proposed and simple universal formulas are derived for the extensions of the theory that include the coupling to noise and the nuclear spin bath.

•Sep 30, 2004•6 citations

Multiple-time-scale Landau-Zener transitions in many-body systems

Jonas Larson

Motivated by recent cold-atom experiments in optical lattices, we consider a lattice version of the Landau-Zener problem. Every single site is described by a Landau-Zener problem, but due to particle tunneling between neighboring lattice sites this on-site single-particle Landau-Zener dynamics couples to the particle motion within the lattice. The lattice, apart from having a dephasing effect on single-site Landau-Zener transitions, also implies, in the presence of a confining trap, an intersite particle flow induced by the Landau-Zener sweeping. This gives rise to an interplay between intra- and intersite dynamics. The adiabaticity constraint is therefore not simply given by the standard one, the Hamiltonian rate of change relative to the gap of the on-site problem. In experimentally realistic situations, the full system evolution is well described by Franck-Condon physics; e.g., nonadiabatic excitations are predominantly external ones characterized by large phononic vibrations in the atomic cloud, while internal excitations are very weak as close-to-perfect on-site transitions take place.

arXiv:1310.7867•Physical Review A•Jan 20, 2015•1 citation

Multistate Landau–Zener problem

Nikolai A. Sinitsyn, V. L. Pokrovsky

Abstract This chapter is introduction to multistate Landau-Zener theory. We prove and solve various general formulas and conclude with a section that describes the solution of the driven Tavis-Cummigs model.

•Feb 5, 2026•0 citations
We formulate and approximately solve a specific many body generalization of the Landau-Zener problem. Unlike with the single particle Landau-Zener problem, our system does not abide in the adiabatic ground state, even at very slow driving rates. The structure of the theory suggests that this finding reflects a more general phenomenon in the physics of adiabatically driven many particle systems. Our solution can be used to understand, for example, the behavior of two-level systems coupled to an electromagnetic field, as realized in cavity QED experiments.
We consider the behavior of an interacting many-particle system under slow external driving---a many-body generalization of the Landau-Zener paradigm. We find that a conspiracy of interactions and driving leads to physics profoundly different from that of the single-particle limit: for practically all values of the driving rate the particle distributions in Hilbert space are very broad, a phenomenon caused by a strong amplification of quantum fluctuations in the driving process. These fluctuations are ``nonadiabatic'' in that even at very slow driving it is exceedingly difficult to push the center of the distribution toward the limit of full ground-state occupancy. We obtain these results by a number of complementary theoretical approaches, including diagrammatic perturbation theory, semiclassical analysis, and exact diagonalization.
Institut fu¨r Theoretische Physik, Universita¨t zu K¨oln, De-50937 K¨oln, Germany(Dated: December 16, 2013)Landau-Zener transitions in a Lipkin-Meshkov-Glick model are considered, both as a single systemand in a lattice where each individual site hosts a realization of the corresponding many-bodyproblem. The single site mean-field problem is conceptually different from many other non-linearLandau-Zener models - it does not support any hysteresis and a new phenomenon appears whereadiabaticity totaly breaks down. More precisely, thisbreakdown occurs for isolated classical solutionspropagating on a separatrix in phase space and during the Landau-Zener sweep they get locked toa fixed point which prohibits adiabatic following. Quantum fluctuations tend to destabilize thesesolutions such that for moderate particle numbers the phenomenon is lost. At the quantum levelit is also shown that the non-adiabatic corrections P of the single site problem obey a power-lawdependenceon the Landau-Zenersweep velocity λ in the adiabatic regime, i.e. P ∼ λ
We study stationary and dynamical properties of the many-body Landau-Zener dynamics of a Bose quantum fluid confined in two coupled one-dimensional chains by using a many-body generalization recently reported Chen et al. [Nature Phys. 7, 61 (2011)], within the decoupling approximation and the one-level band scheme. The energy spectrum shows evidence of the structure of the avoided level crossings as a function of the onsite interparticle interaction strength. On the dynamical side, a phase diagram of the transfer efficiency across ground-state and inverse sweeps is presented. A totally different scenario with respect to the original single-particle Landau-Zener scheme is found for ground-state sweeps, in which a breakdown of the adiabatic region emerges as the sweep rate decreases. On the contrary, the transfer efficiency across inverse sweeps reveals consistent results with the single-particle Landau-Zener predictions. In the strong-coupling regime, we find that there is a critical value of the onsite interaction for which the transfer of particles starts to vanish independently of the sweep rate. Our results are in qualitative agreement with those of the experimental counterpart.
Nanoscale systems have sizes intermediate between atomic and macroscopic ones. Therefore their treatment often requires a combination of methods from atomic and condensed matter physics. The conventional Landau-Zener theory, being a powerful tool in atomic physics, often fails to predict correctly nonadiabatic transition probabilities in various nanostructures because it does not include many-body effects typical for mesoscopics. In this research project the generalizations of the Landau-Zener theory that solve this problem were studied. The multistate, multiparticle and nonunitary extensions of the theory have been proposed and investigated. New classes of exactly solvable models have been derived. I discuss their applications in problems of the molecular condensate dissociation and of the driven charge transport. In application to the physics of nanomagnets new approaches in modeling the influence of the environment on the Landau-Zener evolution are proposed and simple universal formulas are derived for the extensions of the theory that include the coupling to noise and the nuclear spin bath.
Motivated by recent cold-atom experiments in optical lattices, we consider a lattice version of the Landau-Zener problem. Every single site is described by a Landau-Zener problem, but due to particle tunneling between neighboring lattice sites this on-site single-particle Landau-Zener dynamics couples to the particle motion within the lattice. The lattice, apart from having a dephasing effect on single-site Landau-Zener transitions, also implies, in the presence of a confining trap, an intersite particle flow induced by the Landau-Zener sweeping. This gives rise to an interplay between intra- and intersite dynamics. The adiabaticity constraint is therefore not simply given by the standard one, the Hamiltonian rate of change relative to the gap of the on-site problem. In experimentally realistic situations, the full system evolution is well described by Franck-Condon physics; e.g., nonadiabatic excitations are predominantly external ones characterized by large phononic vibrations in the atomic cloud, while internal excitations are very weak as close-to-perfect on-site transitions take place.