Momentum Distributions and One-Body Density Matrices of the Quantum Fluids.

Lukas Rammelmüller, William J. Porter, Jens Braun +1 more

We study the evolution from few- to many-body physics of fermionic systems in one spatial dimension with attractive pairwise interactions. We determine the detailed form of the momentum distribution, the structure of the one-body density matrix, and the pairing properties encoded in the two-body density matrix. From the low- and high-momentum scaling behavior of the single-particle momentum distribution we estimate the speed of sound and Tan's contact, respectively. Both quantities are found to be in agreement with previous calculations. Based on our calculations of the one-body density matrices, we also present results for the particle-partition entanglement entropy, for which we find a logarithmic dependence on the total particle number.

MANFRED L. RISTIG, J. W. Clark

J. W. Clark, MANFRED L. RISTIG

В. А. Головко

The hierarchy of equations for reduced density matrices that describes a thermodynamically equilibrium quantum system obtained earlier by the author is investigated in the momentum representation. In the paper it is shown that the use of the momentum representation opens up new opportunities in studies of macroscopic quantum systems both nonsuperfluid and superfluid. It is found that the distribution over momenta in a quantum fluid is not a Bose or Fermi distribution even in the limit of practically noninteracting particles. The distribution looks like a Maxwellian one although, strictly speaking, it is not Maxwellian. The momentum distribution in a quantum crystal depends upon the interaction potential and the crystalline structure. The momentum distribution in a superfluid contains a delta function. The momentum distribution for the condensate in a superfluid crystal consists of delta peaks that are arranged periodically in momentum space. The periodical structure remains if the condensate crystal is not superfluid.

Bruno Juliá Díaz, Arnau Rios Huguet, Héctor Briongos Merino +2 more

This chapter delves into the concept of density matrices, a fundamental tool in quantum mechanics for describing the state of a many-body system. Density matrices provide a compact and powerful representation of quantum states, encompassing both pure and mixed states. The study of one-body and two-body density matrices is particularly important for understanding the behavior of many-body systems, especially in contexts like quantum gases, solid-state physics, and quantum chemistry. These matrices encapsulate information about particle distributions and correlations, enabling the derivation of key properties such as energy, momentum, and entropy.

R. T. Azuah, H. R. Glyde