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arXiv:2601.12071

Temperature effect on a kicked Tonks-Girardeau gas

Ang Yang, Yue Chen, Lei Ying

quant-phcond-mat.quant-gasSubmitted Jan 17, 2026• Announced Jan 20, 2026• 0 citations
v1 · Jan 17, 2026v2 · Mar 23, 2026
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Abstract

It is widely recognized that finite temperatures degrade quantum coherence and can induce thermalization. Here, we study the effect of finite temperature on a kicked Tonks--Girardeau gas, which is known to exhibit many--body dynamical localization and delocalization under periodic and quasiperiodic kicks, respectively. We find that many--body dynamical localization persists at finite--and even high--temperatures, although the coherence of the localized state is further degraded. In particular, we demonstrate a modified effective thermalization of the localized state by considering the initial temperature. Moreover, we show many--body dynamical localization transition at intermediate temperature. Our work extends the study of many--body dynamical localization and delocalization to the finite--temperature regime, providing comprehensive guidance for cold--atom experiments.

Comments
9 pages, 9 figures

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It is widely recognized that finite temperatures degrade quantum coherence and can induce thermalization. Here, we study the effect of finite temperature on a kicked Tonks--Girardeau gas, which is known to exhibit many--body dynamical localization and delocalization under periodic and quasiperiodic kicks, respectively. We find that many--body dynamical localization persists at finite--and even high--temperatures, although the coherence of the localized state is further degraded. In particular, we demonstrate a modified effective thermalization of the localized state by considering the initial temperature. Moreover, we show many--body dynamical localization transition at intermediate temperature. Our work extends the study of many--body dynamical localization and delocalization to the finite--temperature regime, providing comprehensive guidance for cold--atom experiments.
The quantum kicked rotor is well-known for displaying dynamical (Anderson) localization. It has recently been shown that a periodically kicked Tonks gas will always localize and converge to a finite energy steady-state. This steady-state has been described as being effectively thermal with an effective temperature that depends on the parameters of the kick. Here we study a generalization to a quasi-periodic driving with three frequencies which, without interactions, has a metal-insulator Anderson transition. We show that a quasi-periodically kicked Tonks gas goes through a dynamical many-body delocalization transition when the kick strength is increased. The localized phase is still described by a low effective temperature, while the delocalized phase corresponds to an infinite-temperature phase, with the temperature increasing linearly in time. At the critical point, the momentum distribution of the Tonks gas displays different scaling at small and large momenta (contrary to the non-interacting case), signaling a breakdown of the one-parameter scaling theory of localization.
Dynamical localization is the analog of Anderson localization in momentum space, where the system's energy saturates and the single-particle wave functions are exponentially localized in momentum space. In the presence of interactions, in the context of a periodically kicked Bose gas, it has been argued that dynamical localization persists. Focusing on the Tonks (strongly interacting) regime, we show that the many-body dynamically localized phase is effectively thermal, a clear deviation from the breaking of ergodicity observed in standard many-body localized systems. We relate the effective temperature to the driving parameters, and thus quantitatively describe the loss of coherence at large distances in this phase. Contrary to the noninteracting case, the momentum distribution decays as a power-law at large momenta, characterized by an effectively thermal Tan's contact. This is a rare example where driving and many-body (dynamical) localization lead to an effectively ergodic state.
We study the local correlations in the super Tonks-Girardeau gas, a highly excited, strongly correlated state obtained in quasi-one-dimensional Bose gases by tuning the scattering length to large negative values using a confinement-induced resonance. Exploiting a connection with a relativistic field theory, we obtain results for the two-body and three-body local correlators at zero and finite temperature. At zero temperature, our result for the three-body correlator agrees with the extension of the results of Cheianov et al. [Phys. Rev. A 73, 051604(R) (2006)], obtained for the ground state of the repulsive Lieb-Liniger gas, to the super-Tonks-Girardeau state. At finite temperature, we obtain that the three-body correlator has a weak dependence on temperature up to the degeneracy temperature TD{T}_{\mathrm{D}}TD​. We also find that, for temperatures larger than TD{T}_{\mathrm{D}}TD​, the values of the three-body correlator for the super-Tonks-Girardeau gas and the corresponding repulsive Lieb-Liniger gas are rather similar, even for relatively small couplings.
Ultracold quantum gases offer a fascinating playground for exploring and understanding the fundamentals of out-of-equilibrium behaviour of quantum matter. Experimental systems whose many-body dynamics can be described by exactly solvable models play a particularly important role. A paradigmatic example in this realm is the Tonks-Girardeau (TG) gas of impenetrable bosons. Here we investigate and predict a striking dynamical manifestation of the impenetrability--a collective many-body bounce effect. This effect, while being invisible in the evolution of the in-situ density profile of the gas, can be revealed through a nontrivial narrowing of its momentum distribution during breathing-mode oscillations. To demonstrate this, we develop an exact finite-temperature dynamical theory of a harmonically trapped TG gas, thus extending on previous zero-temperature results and opening the way to solving arbitrary dynamical protocols of the TG gas. We identify physical regimes for observing the many-body bounce effect and foresee it as a valuable probe for characterising the nonequilibrium dynamics of interacting quantum fluids.
Describing finite-temperature nonequilibrium dynamics of interacting many-particle systems is a notoriously challenging problem in quantum many-body physics. Here we provide an exact solution to this problem for a system of strongly interacting bosons in one dimension in the Tonks-Girardeau regime of infinitely strong repulsive interactions. Using the Fredholm determinant approach and the Bose-Fermi mapping, we show how the problem can be reduced to a single-particle basis, wherein the finite-temperature effects enter the solution via an effective ``dressing'' of the single-particle wave functions by the Fermi-Dirac occupation factors. We demonstrate the utility of our approach and its computational efficiency in two nontrivial out-of-equilibrium scenarios: collective breathing-mode oscillations in a harmonic trap and collisional dynamics in the Newton's cradle setting involving real-time evolution in a periodic Bragg potential.
We study the out-of-equilibrium dynamics of a finite-temperature harmonically trapped Tonks-Girardeau gas induced by periodic modulation of the trap frequency. We give explicit exact solutions for the real-space density and momentum distributions of this interacting many-body system and characterize the stability diagram of the dynamics by mapping the many-body solution to the solution and stability diagram of Mathieu's differential equation. The mapping allows one to deduce the exact structure of parametric resonances in the parameter space characterized by the driving amplitude and frequency of the modulation. Furthermore, we analyze the same problem within the finite-temperature hydrodynamic approach and show that the respective solutions to the hydrodynamic equations can be mapped to the same Mathieu equation. Accordingly, the stability diagram and the structure of resonances following from the hydrodynamic approach are exactly the same as those obtained from the exact many-body solution.