We study the mean-field dynamics of a system of $N$ interacting bosons starting from an initially condensated state. For a broad class of mean-field Hamiltonians, including models with arbitrary bounded interactions and models with unbounded interaction potentials, we prove that the probability of having $n$ particles outside the condensate decays exponentially in $n$ for any finite evolution time. Our results strengthen previously known bounds that provide only polynomial control on the probability of having $n$ excitations.We study the mean-field dynamics of a system of $N$ interacting bosons starting from an initially condensated state. For a broad class of mean-field Hamiltonians, including models with arbitrary bounded interactions and models with unbounded interaction potentials, we prove that the probability of having $n$ particles outside the condensate decays exponentially in $n$ for any finite evolution time. Our results strengthen previously known bounds that provide only polynomial control on the probability of having $n$ excitations.

math-phCross-listedarXiv:2602.16658Journal of Mathematical PhysicsFeb 19, 20260 citations

Exponential decay for the bound state wave functions of several particle systems

A. J. O'Connor

University Microfilms International eBooksJan 1, 19722 citations

Reliability Is Not Free in Universal Quantum Work Extraction

Shuai Zeng

Universal work extraction shows that input-state knowledge is unnecessary to attain the asymptotic free-energy rate. We ask whether this first-order universality extends to reliability, the exponential decay rate of extraction failure. In the work-battery fidelity formulation, we prove that no phase-independent Gibbs-preserving protocol can retain the state-aware Gibbs-preserving exponent throughout a coherent qubit time-translation orbit: at every positive target rate, its worst pointwise exponent is bounded by the corresponding state-aware thermal-operation value. The proof first establishes an exact finite-blocklength identity between phase-robust Gibbs-preserving extraction and state-aware thermal extraction. A trigonometric Remez inequality then upgrades this minimax identity to a pointwise theorem by ruling out exponential localization of the worst phase. For an explicit coherent-qubit family, known-phase Gibbs-preserving extraction is error free, whereas every phase-independent protocol has a finite worst-pointwise exponent. Thus input-state knowledge can be irrelevant to the first-order work rate yet indispensable for optimal exponential reliability.Universal work extraction shows that input-state knowledge is unnecessary to attain the asymptotic free-energy rate. We ask whether this first-order universality extends to reliability, the exponential decay rate of extraction failure. In the work-battery fidelity formulation, we prove that no phase-independent Gibbs-preserving protocol can retain the state-aware Gibbs-preserving exponent throughout a coherent qubit time-translation orbit: at every positive target rate, its worst pointwise exponent is bounded by the corresponding state-aware thermal-operation value. The proof first establishes an exact finite-blocklength identity between phase-robust Gibbs-preserving extraction and state-aware thermal extraction. A trigonometric Remez inequality then upgrades this minimax identity to a pointwise theorem by ruling out exponential localization of the worst phase. For an explicit coherent-qubit family, known-phase Gibbs-preserving extraction is error free, whereas every phase-independent protocol has a finite worst-pointwise exponent. Thus input-state knowledge can be irrelevant to the first-order work rate yet indispensable for optimal exponential reliability.

quant-pharXiv:2607.16702Jul 21, 20260 citations

Work statistics and generalized Loschmidt echo for the Hatano-Nelson model

Balázs Dóra, Cătălin Paşcu Moca

We focus on the biorthogonal work statistics of the interacting many-body Hatano-Nelson model after switching on the imaginary vector potential. We introduce a generalized Loschmidt echo $G(t)$ using the biorthogonal metric operator whose Fourier transform yields the probability distribution of work done. The statistics of work displays several universal features, including an exponential decay with the square of both the system size and imaginary vector potential for the probability to stay in the ground state. Additionally, its high-energy tail follows a universal power law with exponent $\ensuremath{-}3$. This originates from the peculiar temporal power-law decay of $G(t)$ with a time-dependent exponent, corresponding to an unusual orthogonality catastrophe. The mean and the variance of work scale linearly and logarithmically with system size, while all higher cumulants are nonextensive. Our results are relevant for nonunitary field theories as well.We focus on the biorthogonal work statistics of the interacting many-body Hatano-Nelson model after switching on the imaginary vector potential. We introduce a generalized Loschmidt echo $G(t)$ using the biorthogonal metric operator whose Fourier transform yields the probability distribution of work done. The statistics of work displays several universal features, including an exponential decay with the square of both the system size and imaginary vector potential for the probability to stay in the ground state. Additionally, its high-energy tail follows a universal power law with exponent $\ensuremath{-}3$. This originates from the peculiar temporal power-law decay of $G(t)$ with a time-dependent exponent, corresponding to an unusual orthogonality catastrophe. The mean and the variance of work scale linearly and logarithmically with system size, while all higher cumulants are nonextensive. Our results are relevant for nonunitary field theories as well.

arXiv:2310.19310Physical review. B./Physical review. BSep 19, 20245 citations

Decay of quantum states in some exactly soluble models

G.C. Stey, R. W. Gibberd

PhysicaJul 1, 197279 citations

We study the mean-field dynamics of a system of

N

interacting bosons starting from an initially condensated state. For a broad class of mean-field Hamiltonians, including models with arbitrary bounded interactions and models with unbounded interaction potentials, we prove that the probability of having

n

particles outside the condensate decays exponentially in

n

for any finite evolution time. Our results strengthen previously known bounds that provide only polynomial control on the probability of having

n

excitations.

We focus on the biorthogonal work statistics of the interacting many-body Hatano-Nelson model after switching on the imaginary vector potential. We introduce a generalized Loschmidt echo

G(t)

using the biorthogonal metric operator whose Fourier transform yields the probability distribution of work done. The statistics of work displays several universal features, including an exponential decay with the square of both the system size and imaginary vector potential for the probability to stay in the ground state. Additionally, its high-energy tail follows a universal power law with exponent $\ensuremath{-}3$. This originates from the peculiar temporal power-law decay of

G(t)

with a time-dependent exponent, corresponding to an unusual orthogonality catastrophe. The mean and the variance of work scale linearly and logarithmically with system size, while all higher cumulants are nonextensive. Our results are relevant for nonunitary field theories as well.