For an imperfect Bose gas consisting of massive particles and interacting through a long-range pair potential in a mean-field approximation, both in equilibrium and far from equilibrium, the dynamics are derived in the thermodynamic limit. This is done in the framework of the operator algebraic quantum theory. The limiting dynamics is formulated in the Schrödinger picture as a group of affine transformations of certain folia of physical states. Similar to the mean-field models for spin lattices, the algebra of quasilocal observables is not invariant under the Heisenberg dynamics in the GNS representation of general time invariant states. It is known that above critical density the infinite system exhibits condensation, and the condensate is characterized by the classical parameters density and phase. For these parameters a classical nonlinear equation of motion is derived.For an imperfect Bose gas consisting of massive particles and interacting through a long-range pair potential in a mean-field approximation, both in equilibrium and far from equilibrium, the dynamics are derived in the thermodynamic limit. This is done in the framework of the operator algebraic quantum theory. The limiting dynamics is formulated in the Schrödinger picture as a group of affine transformations of certain folia of physical states. Similar to the mean-field models for spin lattices, the algebra of quasilocal observables is not invariant under the Heisenberg dynamics in the GNS representation of general time invariant states. It is known that above critical density the infinite system exhibits condensation, and the condensate is characterized by the classical parameters density and phase. For these parameters a classical nonlinear equation of motion is derived.

Journal of Mathematical PhysicsNov 1, 19930 citations

On the existence of solutions of the Brueckner equations for a many-fermion system

Victor J. Emery

Nuclear PhysicsJun 1, 195947 citations

Equation of state of cold atoms: A lowest-order-constrained variational study of systems with large non- s -wave scattering lengths

Ryan M. Kalas, D. Blume

Dilute Fermi systems with large $s$ -wave scattering length ${a}_{s}$ exhibit universal properties if the interparticle spacing ${r}_{0}$ greatly exceeds the range of the underlying two-body interaction potential. In this regime, ${r}_{0}$ is the only relevant length scale and observables such as the energy per particle depend only on ${r}_{0}$ (or, equivalently, the energy ${E}_{\mathrm{FG}}$ of the free Fermi gas). This paper investigates Bose and Fermi systems with nonvanishing angular momentum $l$ using the lowest order constrained variational method. We focus on the regime where the generalized scattering length becomes large and determine the relevant length scales. For Bose gases with large generalized scattering lengths, we obtain simple expressions for the energy per particle in terms of an $l$ -dependent length scale ${\ensuremath{\xi}}_{l}$, which depends on the range of the underlying two-body potential and the average interparticle spacing. We discuss possible implications for dilute two-component Fermi systems with finite $l$ . Furthermore, we determine the equation of state of liquid and gaseous bosonic helium.Dilute Fermi systems with large $s$-wave scattering length ${a}_{s}$ exhibit universal properties if the interparticle spacing ${r}_{0}$ greatly exceeds the range of the underlying two-body interaction potential. In this regime, ${r}_{0}$ is the only relevant length scale and observables such as the energy per particle depend only on ${r}_{0}$ (or, equivalently, the energy ${E}_{\mathrm{FG}}$ of the free Fermi gas). This paper investigates Bose and Fermi systems with nonvanishing angular momentum $l$ using the lowest order constrained variational method. We focus on the regime where the generalized scattering length becomes large and determine the relevant length scales. For Bose gases with large generalized scattering lengths, we obtain simple expressions for the energy per particle in terms of an $l$-dependent length scale ${\ensuremath{\xi}}_{l}$, which depends on the range of the underlying two-body potential and the average interparticle spacing. We discuss possible implications for dilute two-component Fermi systems with finite $l$. Furthermore, we determine the equation of state of liquid and gaseous bosonic helium.

Physical Review AJul 18, 20073 citations

On non-linear Schrödinger equations for open quantum systems

S. V. Mousavi, Salvador Miret-Artés

arXiv:1902.04410The European Physical Journal PlusSep 1, 201912 citations

Approximating observables on eigenstates of large many-body localized systems

Abishek K. Kulshreshtha, Arijeet Pal, Thorsten B. Wahl +1 more

Eigenstates of fully many-body localized (FMBL) systems can be organized into spin algebras based on quasilocal operators called $l$ bits. These spin algebras define quasilocal $l$ -bit measurement (${\ensuremath{\tau}}_{i}^{z}$) and $l$ -bit flip (${\ensuremath{\tau}}_{i}^{x}$) operators. For a disordered Heisenberg spin chain in the MBL regime we approximate $l$ -bit flip operators by first calculating them exactly on small windows of systems using an algorithm called operator localization optimization. We then extend the $l$ -bit operators onto the whole system by exploiting their quasilocal nature. We subsequently use these operators to represent approximate eigenstates of the Hamiltonian. Finally, we describe a method to calculate products of local observables on these eigenstates for systems of size $L$ in $O({L}^{2})$ time. This method is used to calculate the variance of the energy of the approximate eigenstates, yielding an estimate of the error of the approximation.Eigenstates of fully many-body localized (FMBL) systems can be organized into spin algebras based on quasilocal operators called $l$ bits. These spin algebras define quasilocal $l$-bit measurement (${\ensuremath{\tau}}_{i}^{z}$) and $l$-bit flip (${\ensuremath{\tau}}_{i}^{x}$) operators. For a disordered Heisenberg spin chain in the MBL regime we approximate $l$-bit flip operators by first calculating them exactly on small windows of systems using an algorithm called operator localization optimization. We then extend the $l$-bit operators onto the whole system by exploiting their quasilocal nature. We subsequently use these operators to represent approximate eigenstates of the Hamiltonian. Finally, we describe a method to calculate products of local observables on these eigenstates for systems of size $L$ in $O({L}^{2})$ time. This method is used to calculate the variance of the energy of the approximate eigenstates, yielding an estimate of the error of the approximation.

arXiv:1811.00442Physical review. B./Physical review. BMar 11, 201914 citations

THE VARIATIONAL SOLUTION OF THE SCHROEDINGER EQUATION OF FINITE FERMION SYSTEMS

John Frederick Schroeder

Jan 1, 19710 citations

Dilute Fermi systems with large

s

-wave scattering length

{a}_{s}

exhibit universal properties if the interparticle spacing

{r}_{0}

greatly exceeds the range of the underlying two-body interaction potential. In this regime,

{r}_{0}

is the only relevant length scale and observables such as the energy per particle depend only on

{r}_{0}

(or, equivalently, the energy

{E}_{\mathrm{FG}}

of the free Fermi gas). This paper investigates Bose and Fermi systems with nonvanishing angular momentum

l

using the lowest order constrained variational method. We focus on the regime where the generalized scattering length becomes large and determine the relevant length scales. For Bose gases with large generalized scattering lengths, we obtain simple expressions for the energy per particle in terms of an

l

-dependent length scale ${\ensuremath{\xi}}_{l}$, which depends on the range of the underlying two-body potential and the average interparticle spacing. We discuss possible implications for dilute two-component Fermi systems with finite

l

. Furthermore, we determine the equation of state of liquid and gaseous bosonic helium.

Eigenstates of fully many-body localized (FMBL) systems can be organized into spin algebras based on quasilocal operators called

l

bits. These spin algebras define quasilocal

l

-bit measurement (${\ensuremath{\tau}}_{i}^{z}$) and

l

-bit flip (${\ensuremath{\tau}}_{i}^{x}$) operators. For a disordered Heisenberg spin chain in the MBL regime we approximate

l

-bit flip operators by first calculating them exactly on small windows of systems using an algorithm called operator localization optimization. We then extend the

l

-bit operators onto the whole system by exploiting their quasilocal nature. We subsequently use these operators to represent approximate eigenstates of the Hamiltonian. Finally, we describe a method to calculate products of local observables on these eigenstates for systems of size

L

O({L}^{2})

time. This method is used to calculate the variance of the energy of the approximate eigenstates, yielding an estimate of the error of the approximation.