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:2405.04789 · Physical Review A

Universality and two-body losses: Lessons from the effective non-Hermitian dynamics of two particles

Alice Marché, Hironobu Yoshida, Alberto Nardin, Hosho Katsura, Leonardo Mazza

Published Sep 19, 2024• 11 citations
arXivHTMLPDF

Abstract

We study the late-time dynamics of two particles confined in one spatial dimension and subject to two-body losses. The dynamics is exactly described by a non-Hermitian Hamiltonian that can be analytically studied both in the continuum and on a lattice. The asymptotic decay rate and the universal power-law form of the decay of the number of particles are exactly computed in the whole parameter space of the problem. When in the initial state the two particles are far apart, the average number of particles in the setup decays with time $t$ as ${t}^{\ensuremath{-}1/2}$; a different power law, ${t}^{\ensuremath{-}3/2}$, is found when the two particles overlap in the initial state. These results are valid both in the continuum and on a lattice, but in the latter case a logarithmic correction appears.

DOI
10.1103/physreva.110.033321

Related papers

Dynamical theory for one-dimensional fermions with strong two-body losses: Universal non-Hermitian Zeno physics and spin-charge separation

Lorenzo Rosso, Alberto Biella, Jacopo De Nardis +1 more

We study an interacting one-dimensional gas of spin-1/2 fermions with two-body losses. The dynamical phase diagram that characterizes the approach to the stationary state displays a wide quantum Zeno region, identified by a peculiar behavior of the lowest eigenvalues of the associated non-Hermitian Hamiltonian. We characterize the universal dynamics of this Zeno regime using an approximation scheme based on an effective decoupling of charge and spin degrees of freedom, where the latter effectively evolve according to a non-Hermitian Heisenberg Hamiltonian. We present detailed results for the time evolution from initial states with one particle per site with either incoherent or antiferromagnetic spin order, showing how peculiar charge properties witnessed by the momentum distribution function build up in time.

arXiv:2206.06837•Physical Review A•Jan 6, 2023•30 citations

Topological properties of single-particle states decaying into a continuum due to interaction

Bilal Hawashin, Jesko Sirker, Götz Silvester Uhrig

We investigate how topological Chern numbers can be defined when single-particle states hybridize with continua. We do so exemplarily in a bosonic Haldane model at zero temperature with an additional on-site decay of one boson into two and the conjugate fusion of two bosons into one. Restricting the Hilbert space to two bosons at maximum, the exact self-energy is accessible. We use the bilinear Hamiltonian H 0 corrected by the self-energy Σ to compute Chern numbers by two different approaches. The results are gauged against a full many-body calculation in the Hilbert space where possible. We establish numerically and analytically that the effective Hamiltonian H eff = H 0 ( k ⃗ ) + Σ ( ω , k ⃗ ) reproduces the correct many-body topology if the considered band does not overlap with the continuum. In case of overlaps, one can extend the definition of the Chern number to the non-Hermitian H eff and there is evidence that the Chern number changes at exceptional points. But the bulk-boundary correspondence appears to be no longer valid and edge modes delocalize. Published by the American Physical Society 2024

arXiv:2310.09957•Physical Review Research•Nov 12, 2024•2 citations

Universal Loss Dynamics of a Degenerate Homogeneous Unitary Bose Gas

Christoph Eigen, Jake Glidden, Raphael Lopes +4 more

Bulletin of the American Physical Society•Jun 7, 2017•0 citations

Universal and non-universal effective N-body interactions for ultracold harmonically-trapped few-atom systems

Xiangyu Yin, D. Blume, Philip Johnson +1 more

New Journal of Physics•Oct 28, 2014•1 citation

Failure of the mean-field Hartree approximation for a bosonic many-body system with non-Hermitian Hamiltonian

Matias Ginzburg, Simone Rademacher, Giacomo De Palma

Mean-field Hartree theory is a central tool for reducing many-body dynamics to an effective one-particle evolution. This approximation has been employed when the Hamiltonian governing the many-body dynamics is not Hermitian. Indeed, non-Hermitian Hamiltonians model particle gain/loss or the evolution of open quantum systems between consecutive quantum jumps. Furthermore, the validity of the Hartree approximation for generic non-Hermitian Hamiltonians lies at the basis of a quantum algorithm for nonlinear differential equations. In this work, we show that this approximation can fail. First, we consider the most general bosonic mean-field Hamiltonian with two-body interactions and we prove that, for non-Hermitian Hamiltonian, the Hartree equation does not capture the correct second time derivative of the one-particle marginal state at $t=0$ in the thermodynamic limit. Then, we analytically solve a model of $N$ bosonic qubits with a purely anti-Hermitian Hamiltonian, compute the limit for $N\to\infty$ of the one-particle marginal state and show that it does not agree with the solution of the non-Hermitian Hartree equation. We further show that there exists an initial condition such that the exact one-particle marginal state undergoes a finite-time transition to a mixed state, a phenomenon that is completely absent in the case of Hermitian Hamiltonians. Finally, we simulate a non-Hermitian Hamiltonian with real spectrum and show that, also in this case, there are initial conditions for which the Hartree equation does not reproduce the correct one-particle marginal state in the limit $N\to\infty$. Our findings challenge the validity of the mean-field Hartree approximation for non-Hermitian Hamiltonians, and call for additional conditions for the validity of the mean-field regime to model the dynamics of particle gain and loss and the open-system dynamics in bosonic many-body systems.

quant-pharXiv:2601.13038•Quantum•Jan 20, 2026•0 citations

Quantum reaction-limited reaction-diffusion dynamics of annihilation processes

Gabriele Perfetto, Federico Carollo, Juan P. Garrahan +1 more

We investigate the quantum reaction-diffusion dynamics of fermionic particles which coherently hop in a one-dimensional lattice and undergo annihilation reactions. The latter are modelled as dissipative processes which involve losses of pairs 2A→∅, triplets 3A→∅, and quadruplets 4A→∅ of neighboring particles. When considering classical particles, the corresponding decay of their density in time follows an asymptotic power-law behavior. The associated exponent in one dimension is different from the mean-field prediction whenever diffusive mixing is not too strong and spatial correlations are relevant. This specifically applies to 2A→∅, while the mean-field power-law prediction just acquires a logarithmic correction for 3A→∅ and is exact for 4A→∅. A mean-field approach is also valid, for all the three processes, when the diffusive mixing is strong, i.e., in the so-called reaction-limited regime. Here we show that the picture is different for quantum systems. We consider the quantum reaction-limited regime and we show that for all the three processes power-law behavior beyond mean field is present as a consequence of quantum coherences, which are not related to space dimensionality. The decay in 3A→∅ is further, highly intricate, since the power-law behavior therein only appears within an intermediate time window, while at long times the density decay is not power law. Our results show that emergent critical behavior in quantum dynamics has a markedly different origin, based on quantum coherences, to that applying to classical critical phenomena, which is, instead, solely determined by the relevance of spatial correlations.

arXiv:2305.06944•Physical review. E•Dec 4, 2023•13 citations
We study the late-time dynamics of two particles confined in one spatial dimension and subject to two-body losses. The dynamics is exactly described by a non-Hermitian Hamiltonian that can be analytically studied both in the continuum and on a lattice. The asymptotic decay rate and the universal power-law form of the decay of the number of particles are exactly computed in the whole parameter space of the problem. When in the initial state the two particles are far apart, the average number of particles in the setup decays with time ttt as t\ensuremath−1/2{t}^{\ensuremath{-}1/2}t\ensuremath−1/2; a different power law, t\ensuremath−3/2{t}^{\ensuremath{-}3/2}t\ensuremath−3/2, is found when the two particles overlap in the initial state. These results are valid both in the continuum and on a lattice, but in the latter case a logarithmic correction appears.
We study an interacting one-dimensional gas of spin-1/2 fermions with two-body losses. The dynamical phase diagram that characterizes the approach to the stationary state displays a wide quantum Zeno region, identified by a peculiar behavior of the lowest eigenvalues of the associated non-Hermitian Hamiltonian. We characterize the universal dynamics of this Zeno regime using an approximation scheme based on an effective decoupling of charge and spin degrees of freedom, where the latter effectively evolve according to a non-Hermitian Heisenberg Hamiltonian. We present detailed results for the time evolution from initial states with one particle per site with either incoherent or antiferromagnetic spin order, showing how peculiar charge properties witnessed by the momentum distribution function build up in time.
We investigate how topological Chern numbers can be defined when single-particle states hybridize with continua. We do so exemplarily in a bosonic Haldane model at zero temperature with an additional on-site decay of one boson into two and the conjugate fusion of two bosons into one. Restricting the Hilbert space to two bosons at maximum, the exact self-energy is accessible. We use the bilinear Hamiltonian H 0 corrected by the self-energy Σ to compute Chern numbers by two different approaches. The results are gauged against a full many-body calculation in the Hilbert space where possible. We establish numerically and analytically that the effective Hamiltonian H eff = H 0 ( k ⃗ ) + Σ ( ω , k ⃗ ) reproduces the correct many-body topology if the considered band does not overlap with the continuum. In case of overlaps, one can extend the definition of the Chern number to the non-Hermitian H eff and there is evidence that the Chern number changes at exceptional points. But the bulk-boundary correspondence appears to be no longer valid and edge modes delocalize. Published by the American Physical Society 2024
Mean-field Hartree theory is a central tool for reducing many-body dynamics to an effective one-particle evolution. This approximation has been employed when the Hamiltonian governing the many-body dynamics is not Hermitian. Indeed, non-Hermitian Hamiltonians model particle gain/loss or the evolution of open quantum systems between consecutive quantum jumps. Furthermore, the validity of the Hartree approximation for generic non-Hermitian Hamiltonians lies at the basis of a quantum algorithm for nonlinear differential equations. In this work, we show that this approximation can fail. First, we consider the most general bosonic mean-field Hamiltonian with two-body interactions and we prove that, for non-Hermitian Hamiltonian, the Hartree equation does not capture the correct second time derivative of the one-particle marginal state at t=0t=0t=0 in the thermodynamic limit. Then, we analytically solve a model of NNN bosonic qubits with a purely anti-Hermitian Hamiltonian, compute the limit for N→∞N\to\inftyN→∞ of the one-particle marginal state and show that it does not agree with the solution of the non-Hermitian Hartree equation. We further show that there exists an initial condition such that the exact one-particle marginal state undergoes a finite-time transition to a mixed state, a phenomenon that is completely absent in the case of Hermitian Hamiltonians. Finally, we simulate a non-Hermitian Hamiltonian with real spectrum and show that, also in this case, there are initial conditions for which the Hartree equation does not reproduce the correct one-particle marginal state in the limit N→∞N\to\inftyN→∞. Our findings challenge the validity of the mean-field Hartree approximation for non-Hermitian Hamiltonians, and call for additional conditions for the validity of the mean-field regime to model the dynamics of particle gain and loss and the open-system dynamics in bosonic many-body systems.
We investigate the quantum reaction-diffusion dynamics of fermionic particles which coherently hop in a one-dimensional lattice and undergo annihilation reactions. The latter are modelled as dissipative processes which involve losses of pairs 2A→∅, triplets 3A→∅, and quadruplets 4A→∅ of neighboring particles. When considering classical particles, the corresponding decay of their density in time follows an asymptotic power-law behavior. The associated exponent in one dimension is different from the mean-field prediction whenever diffusive mixing is not too strong and spatial correlations are relevant. This specifically applies to 2A→∅, while the mean-field power-law prediction just acquires a logarithmic correction for 3A→∅ and is exact for 4A→∅. A mean-field approach is also valid, for all the three processes, when the diffusive mixing is strong, i.e., in the so-called reaction-limited regime. Here we show that the picture is different for quantum systems. We consider the quantum reaction-limited regime and we show that for all the three processes power-law behavior beyond mean field is present as a consequence of quantum coherences, which are not related to space dimensionality. The decay in 3A→∅ is further, highly intricate, since the power-law behavior therein only appears within an intermediate time window, while at long times the density decay is not power law. Our results show that emergent critical behavior in quantum dynamics has a markedly different origin, based on quantum coherences, to that applying to classical critical phenomena, which is, instead, solely determined by the relevance of spatial correlations.