Condensed matter physics is a rich field with a wide variety of phenomena. In condensed matter, we consider systems composed of many electrons and nuclei, with the only fundamental interaction being electromagnetism. Nuclei of a given charge and mass are considered as point particles. The relevant fundamental physics that we use as our foundations is the quantum many-body problem. That is, just standard many-body quantum mechanics, but formulated in terms of a useful second quantized field theory, which can deal with an arbitrary number of particles within a single Hilbert space. In general, this many-body problem is essentially intractable for numbers of particles as large as those we must consider for materials. Thus we must look for simplifications and look at easily measurable aspects which allow us to make predictions still. We employ the trick of phrasing the questions differently. Rather than look at the time evolution of an arbitrary many-body wavefunction for the fundamental degrees of freedom, we look at transport in scenarios where the starting point is a relatively simple assumed equilibrium state of the material, consisting of a ground state with postulated quasiparticle excitations.Condensed matter physics is a rich field with a wide variety of phenomena. In condensed matter, we consider systems composed of many electrons and nuclei, with the only fundamental interaction being electromagnetism. Nuclei of a given charge and mass are considered as point particles. The relevant fundamental physics that we use as our foundations is the quantum many-body problem. That is, just standard many-body quantum mechanics, but formulated in terms of a useful second quantized field theory, which can deal with an arbitrary number of particles within a single Hilbert space. In general, this many-body problem is essentially intractable for numbers of particles as large as those we must consider for materials. Thus we must look for simplifications and look at easily measurable aspects which allow us to make predictions still. We employ the trick of phrasing the questions differently. Rather than look at the time evolution of an arbitrary many-body wavefunction for the fundamental degrees of freedom, we look at transport in scenarios where the starting point is a relatively simple assumed equilibrium state of the material, consisting of a ground state with postulated quasiparticle excitations.

Aug 1, 20260 citations

Projection on particle number and angular momentum: Example of triaxial Bogoliubov quasiparticle states

B. Bally, M. Bender

The authors provide a state-of-the-art overview of projection techniques employed in beyond-mean-field many-body methods. They focus on two symmetries that are of critical importance for the description of nuclear spectroscopy, particle number, and angular momentum. The presentation covers formal aspects of symmetry restoration (group theory) and practical aspects related to numerical implementation. A number of illustrative examples are given, including cranked states in odd- $A$ nuclei.The authors provide a state-of-the-art overview of projection techniques employed in beyond-mean-field many-body methods. They focus on two symmetries that are of critical importance for the description of nuclear spectroscopy, particle number, and angular momentum. The presentation covers formal aspects of symmetry restoration (group theory) and practical aspects related to numerical implementation. A number of illustrative examples are given, including cranked states in odd-$A$ nuclei.

arXiv:2010.15224Physical Review CFeb 15, 202159 citations

One-particle motion in nuclear many-body problem

育子浜本

Jan 1, 20090 citations

Entanglement entropy, single-particle occupation probabilities, and short-range correlations

Aurel Bulgac

For quantum many-body systems with short-range correlations (SRCs), the intimate relationship between their magnitude, the behavior of the single-particle occupation probabilities at momenta larger than the Fermi momentum, and the entanglement entropy is a new qualitative aspect not studied and exploited yet. A large body of recent condensed matter studies indicates that the time evolution of the entanglement entropy describes the nonequilibrium dynamics of isolated and strongly interacting many-body systems, in a manner similar to the Boltzmann entropy, which is strictly defined for dilute and weakly interacting many-body systems. Both theoretical and experimental studies in nuclei and cold atomic gases have shown that the fermion momentum distribution has a generic behavior $n(k)=C/{k}^{4}$ at momenta larger than the Fermi momentum, due to the presence of SRCs, with approximately 20% of the particles having momenta larger than the Fermi momentum. The presence of the long momentum tails in the presence of SRCs changes the textbook relation between the single-particle kinetic energy and occupation probabilities, ${n}_{\text{mf}}(k)=1/{1+exp\ensuremath{\beta}[\ensuremath{\epsilon}(k)\ensuremath{-}\ensuremath{\mu}]}$ for momenta very different form the Fermi momentum, particularly for dynamics processes. SRCs induced high-momentum tails of the single-particle occupation probabilities increase the entanglement entropy of fermionic systems, which in its turn affects the dynamics of many nuclear reactions, such as heavy-ion collisions and nuclear fission.For quantum many-body systems with short-range correlations (SRCs), the intimate relationship between their magnitude, the behavior of the single-particle occupation probabilities at momenta larger than the Fermi momentum, and the entanglement entropy is a new qualitative aspect not studied and exploited yet. A large body of recent condensed matter studies indicates that the time evolution of the entanglement entropy describes the nonequilibrium dynamics of isolated and strongly interacting many-body systems, in a manner similar to the Boltzmann entropy, which is strictly defined for dilute and weakly interacting many-body systems. Both theoretical and experimental studies in nuclei and cold atomic gases have shown that the fermion momentum distribution has a generic behavior $n(k)=C/{k}^{4}$ at momenta larger than the Fermi momentum, due to the presence of SRCs, with approximately 20% of the particles having momenta larger than the Fermi momentum. The presence of the long momentum tails in the presence of SRCs changes the textbook relation between the single-particle kinetic energy and occupation probabilities, ${n}_{\text{mf}}(k)=1/{1+exp\ensuremath{\beta}[\ensuremath{\epsilon}(k)\ensuremath{-}\ensuremath{\mu}]}$ for momenta very different form the Fermi momentum, particularly for dynamics processes. SRCs induced high-momentum tails of the single-particle occupation probabilities increase the entanglement entropy of fermionic systems, which in its turn affects the dynamics of many nuclear reactions, such as heavy-ion collisions and nuclear fission.

arXiv:2203.12079Physical Review CJun 21, 202335 citations

Lectures on the many-body problem in nuclear physics

L. Rosenfeld, J. Bro-Jørgensen, A. Haatuft +1 more

NORDITA (Nordisk institut for teoretisk atomfysik) eBooksJan 1, 19590 citations

A

nuclei.

n(k)=C/{k}^{4}

at momenta larger than the Fermi momentum, due to the presence of SRCs, with approximately 20% of the particles having momenta larger than the Fermi momentum. The presence of the long momentum tails in the presence of SRCs changes the textbook relation between the single-particle kinetic energy and occupation probabilities, ${n}_{\text{mf}}(k)=1/{1+exp\ensuremath{\beta}[\ensuremath{\epsilon}(k)\ensuremath{-}\ensuremath{\mu}]}$ for momenta very different form the Fermi momentum, particularly for dynamics processes. SRCs induced high-momentum tails of the single-particle occupation probabilities increase the entanglement entropy of fermionic systems, which in its turn affects the dynamics of many nuclear reactions, such as heavy-ion collisions and nuclear fission.