Exact quantum dynamics of yrast states in the finite 1D Bose gas

Kaminishi, Eriko; Sato, Jun; Deguchi, Tetsuo

doi:10.1088/1742-6596/497/1/012030

Cited by 3 publications

(3 citation statements)

References 71 publications

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“…Similar approximations have been applied in the well-studied yrast states. [54][55][56][57][58] Time evolution protocol.-Our aim is to compute the impurity density profile when the initial state (4) is time-evolved according to the Hamiltonian (1)…”

mentioning

confidence: 99%

Motion of a Distinguishable Impurity in the Bose Gas: Arrested Expansion Without a Lattice and Impurity Snaking

2016

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We consider the real time dynamics of an initially localized distinguishable impurity injected into the ground state of the Lieb-Liniger model. Focusing on the case where integrability is preserved, we numerically compute the time evolution of the impurity density operator in regimes far from analytically tractable limits. We find that the injected impurity undergoes a stuttering motion as it moves and expands. For an initially stationary impurity, the interaction-driven formation of a quasibound state with a hole in the background gas leads to arrested expansion -a period of quasistationary behavior. When the impurity is injected with a finite center of mass momentum, the impurity moves through the background gas in a snaking manner, arising from a quantum Newton's cradle-like scenario where momentum is exchanged back-and-forth between the impurity and the background gas.Introduction.-With recent experimental advances in the field of cold atomic gases, the physics of the onedimensional Bose gas is receiving an increasing amount of attention.1-15 These systems, in which one has unprecedented isolation from the environment and fine control of interparticle interactions, are excellent tools for examining novel phenomena arising from strong correlations.One such phenomenon which has piqued both theoretical 8,14,[16][17][18][19][20][21] and experimental 19,22 curiosity is the expansion dynamics of a gas of cold atoms. A number of surprising and interesting effects have been observed, of which arrested expansion (or self trapping)16-18 is of particular relevance to this work. A gas (bosons 19 or fermions 23,24 ) is released from a confining potential and allowed to expand on the lattice. Under this time evolution 'bimodal' expansion is observed: the sparse outer regions of the cloud rapidly expand whilst the dense central region spreads only very slowly. This can be partially understood by considering the limit of strong interactions: doubly occupied sites are high energy configurations which, thanks to the lattice imposing a finite bandwidth and energy conservation, cannot release their energy to the rest of the system and decay. 18With these recent experimental advances 25 has also come the ability to examine systems in which there is a large imbalance between two species; 6,7,9,26-29 a natural starting point for the study of impurity physics. This gives insight in to a diverse range of problems, 29 from the physics of polarons 27,30 to the x-ray edge singularity 31,32 and the orthogonality catastrophe. 33 The physics of impurities also plays an important role in the calculation of edge exponents in dynamical correlation functions 34 and in understanding the nonequilibrium dynamics following a local quantum quench. 13,35,36The experimental study of the out-of-equilibrium dynamics of a single impurity in the one-dimensional Bose gas has revealed rather rich physics: from how an impurity spreads when accelerated through a Tonks-Girardeau gas, 6 to how interactions effect oscillations in the size of a trapped out-of-e...

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confidence: 99%

Motion of a Distinguishable Impurity in the Bose Gas: Arrested Expansion Without a Lattice and Impurity Snaking

2016

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“…In proposing the initial state (23), we were motivated by the construction of a density notch in the Lieb-Liniger model [115,[144][145][146]. Here we show that the state (23) with the Fermi sea of integers {I} is a natural generalization of (21): there is a notch in the density of the majority σ =↑ species, which is accompanied by a localized particle density in the minority σ =↓ species.…”

Section: Particle Densities In the Initial Statementioning

confidence: 97%

“…In [115,[144][145][146] the states (21) were used to study the dynamics of a density notch (sometimes called a 'dark soliton'). This included studies of how the notch dissolves in time, and the finite-size recurrences that occur during unitary time-evolution.…”

Section: Initially Localized States In the Lieb-liniger Modelmentioning

confidence: 99%

Light cone dynamics in excitonic states of two-component Bose and Fermi gases

Robinson¹,

Caux²,

Konik³

2020

J. Stat. Mech.

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We consider the non-equilibrium dynamics of two-component one dimensional quantum gases in the limit of extreme population imbalance where the minority species has but a single particle. We consider the situation where the gas is prepared in a state with a single spatially localized exciton: the single particle of the minority species is spatially localized while the density of the majority species in the vicinity of the minority particle sees a depression. Remarkably, we are able to consider cases where the gas contains on the order of N = 100 particles, comparable to that studied in experiments on cold atomic gases. We are able to do so by exploiting the integrability of the gas together with the observation that the excitonic state can be constructed through a simple superposition of exact eigenstates of the gas. The number of states in this superposition, rather than being exponentially large in the number of particles, scales linearly with N.We study the evolution of such spatially localized states in both strongly interacting Bose and Fermi gases. The behavior of the light cones when the interaction strength and density of the gas is varied can be understood from exact results for the spin excitation spectrum in these systems. We argue that the light cone in both cases exhibits scaling collapse. However unique to the Bose gas, we show that the presence of gapped finite-momentum roton-like excitations provide the Bose gas dynamics with secondary light cones.

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Hohenberg-Kohn theorems in electrostatic and uniform magnetostatic fields

Pan

Sahni

2015

The Journal of Chemical Physics

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The Hohenberg-Kohn (HK) theorems of bijectivity between the external scalar potential and the gauge invariant nondegenerate ground state density, and the consequent Euler variational principle for the density, are proved for arbitrary electrostatic field and the constraint of fixed electron number. The HK theorems are generalized for spinless electrons to the added presence of an external uniform magnetostatic field by introducing the new constraint of fixed canonical orbital angular momentum. Thereby, a bijective relationship between the external scalar and vector potentials, and the gauge invariant nondegenerate ground state density and physical current density, is proved. A corresponding Euler variational principle in terms of these densities is also developed. These theorems are further generalized to electrons with spin by imposing the added constraint of fixed canonical orbital and spin angular momenta. The proofs differ from the original HK proof and explicitly account for the many-to-one relationship between the potentials and the nondegenerate ground state wave function. A Percus-Levy-Lieb constrained-search proof expanding the domain of validity to N-representable functions, and to degenerate states, again for fixed electron number and angular momentum, is also provided.

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Exact quantum dynamics of yrast states in the finite 1D Bose gas

Cited by 3 publications

References 71 publications

Motion of a Distinguishable Impurity in the Bose Gas: Arrested Expansion Without a Lattice and Impurity Snaking

Motion of a Distinguishable Impurity in the Bose Gas: Arrested Expansion Without a Lattice and Impurity Snaking

Light cone dynamics in excitonic states of two-component Bose and Fermi gases

Hohenberg-Kohn theorems in electrostatic and uniform magnetostatic fields

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