Quantum Few-body Systems

The eigenstate thermalization hypothesis (ETH), which asserts that every eigenstate of a many-body quantum system is indistinguishable from a thermal ensemble, plays a pivotal role in understanding thermalization of isolated quantum systems. Yet, no evidence has been obtained as to whether the ETH holds for all few-body operators in a chaotic system; such few-body operators include key quantities in statistical mechanics, such as the total magnetization, the momentum distributions, and their low-order thermal and quantum fluctuations. Here, we formulate a conjecture that for a generic nonintegrable system the ETH holds simultaneously for all $m$ -body operators with $m < α_{\ast} N$ in the thermodynamic limit for some nonzero constant $α_{\ast} > 0$ . We first show the existence of such nontrivial constants for idealized (pseudo) random-matrix descriptions of many-body eigenstates. We then verify the conjecture for generic spin, Bose, and Fermi systems with local and few-body interactions by large-scale numerical calculations. Our results imply that generic systems satisfy the ETH simultaneously for all few-body operators, including their thermal and quantum fluctuations.The eigenstate thermalization hypothesis (ETH), which asserts that every eigenstate of a many-body quantum system is indistinguishable from a thermal ensemble, plays a pivotal role in understanding thermalization of isolated quantum systems. Yet, no evidence has been obtained as to whether the ETH holds for all few-body operators in a chaotic system; such few-body operators include key quantities in statistical mechanics, such as the total magnetization, the momentum distributions, and their low-order thermal and quantum fluctuations. Here, we formulate a conjecture that for a generic nonintegrable system the ETH holds simultaneously for all $m$-body operators with $m < α_{\ast} N$ in the thermodynamic limit for some nonzero constant $α_{\ast} > 0$. We first show the existence of such nontrivial constants for idealized (pseudo) random-matrix descriptions of many-body eigenstates. We then verify the conjecture for generic spin, Bose, and Fermi systems with local and few-body interactions by large-scale numerical calculations. Our results imply that generic systems satisfy the ETH simultaneously for all few-body operators, including their thermal and quantum fluctuations.

arXiv:2303.10069Mar 17, 20231 citation

Quantum Many Body Systems

Vincent Rivasseau, Robert Seiringer, Jan Philip Solovej +1 more

Lecture notes in mathematicsJan 1, 201212 citations

Quantum few-body systems : proceedings of the Joint Physics/Mathematics Workshop on Quantum Few-Body Systems, Aarhus, Denmark, 19-20 March 2007

Joint Physics, Jacob Schach Møller, Dmitiri Fedorov

All papers have been peer-reviewed. The purpose of the workshop was to bring together and promote cooperation between theoretical physicists and mathematicians. Half of the talks were presented by mathematicians, the other half by physicists with the unifying theme being the field of Quantum few-body systems. The field is conceptually understood as applications of rigorous ab-initio methods to quantum systems consisting of a relatively small number of well-defined constituents and is of interest for both mathematicians and physicists.All papers have been peer-reviewed. The purpose of the workshop was to bring together and promote cooperation between theoretical physicists and mathematicians. Half of the talks were presented by mathematicians, the other half by physicists with the unifying theme being the field of Quantum few-body systems. The field is conceptually understood as applications of rigorous ab-initio methods to quantum systems consisting of a relatively small number of well-defined constituents and is of interest for both mathematicians and physicists.

AIP eBooksJan 1, 20080 citations

Few-body dipole-octopole interactions

Jianing Han

We report on the few-body dipole-octopole interactions in excited states. Dipole-octopole interactions of up to ten bodies have been calculated. It has been shown that such a system is an ideal quantum system, which can be accurately generalised to more bodies. In addition, pure repulsive states are shown, and the repulsion strength can be increased by increasing the number of atoms. Moreover, this system can be used for manufacturing more compact quantum computers. Furthermore, it can be used to store quantum information or study entangled states.We report on the few-body dipole-octopole interactions in excited states. Dipole-octopole interactions of up to ten bodies have been calculated. It has been shown that such a system is an ideal quantum system, which can be accurately generalised to more bodies. In addition, pure repulsive states are shown, and the repulsion strength can be increased by increasing the number of atoms. Moreover, this system can be used for manufacturing more compact quantum computers. Furthermore, it can be used to store quantum information or study entangled states.

Molecular PhysicsMay 15, 20230 citations

m

-body operators with

m < α_{\ast} N

in the thermodynamic limit for some nonzero constant

α_{\ast} > 0

. We first show the existence of such nontrivial constants for idealized (pseudo) random-matrix descriptions of many-body eigenstates. We then verify the conjecture for generic spin, Bose, and Fermi systems with local and few-body interactions by large-scale numerical calculations. Our results imply that generic systems satisfy the ETH simultaneously for all few-body operators, including their thermal and quantum fluctuations.