# Massive Fermi Gas in the Expanding Universe [CEA]

The behavior of a decoupled ideal Fermi gas in a homogeneously expanding three-dimensional volume is investigated, starting from an equilibrium spectrum. In case the gas is massless and/or completely degenerate, the spectrum of the gas can be described by an effective temperature and/or an effective chemical potential, both of which scale down with the volume expansion. In contrast, the spectrum of a decoupled massive and non-degenerate gas can only be described by an effective temperature if there are strong enough self-interactions such as to maintain an equilibrium distribution. Assuming perpetual equilibration, we study a decoupled gas which is relativistic at decoupling and then is red-shifted until it becomes non-relativistic. We find expressions for the effective temperature and effective chemical potential which allow us to calculate the final spectrum for arbitrary initial conditions. This calculation is enabled by a new expansion of the Fermi-Dirac integral, which is for our purpose superior to the well-known Sommerfeld expansion. We also compute the behavior of the phase space density under expansion and compare it to the case of real temperature and real chemical potential. Using our results for the degenerate case, we also obtain the mean relic velocity of the recently proposed non-thermal cosmic neutrino background.

A. Trautner
Thu, 22 Dec 16
21/65

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# Microscopic Study of ${}^1{S_0}$ Superfluidity in Dilute Neutron Matter [CL]

Singlet $S$-wave superfluidity of dilute neutron matter is studied within the correlated BCS method, which takes into account both pairing and short-range correlations. First, the equation of state (EOS) of normal neutron matter is calculated within the Correlated Basis Function (CBF) method in lowest cluster order using the ${}^1{S_0}$ and ${}^3P$ components of the Argonne $V_{18}$ potential, assuming trial Jastrow-type correlation functions. The ${}^1{S_0}$ superfluid gap is then calculated with the corresponding component of the Argonne $V_{18}$ potential and the optimally determined correlation functions. The dependence of our results on the chosen forms for the correlation functions is studied, and the role of the $P$-wave channel is investigated. Where comparison is meaningful, the values obtained for the ${}^1{S_0}$ gap within this simplified scheme are consistent with the results of similar and more elaborate microscopic methods.

G. Pavlou, E. Mavrommatis, C. Moustakidis, et. al.
Thu, 8 Dec 16
35/69

# Unitary Gas Constraints on Nuclear Symmetry Energy [CL]

We show the existence of a lower bound on the volume symmetry energy parameter $S_0$ from unitary gas considerations. We further demonstrate that values of $S_0$ above this minimum imply upper and lower bounds on the symmetry energy parameter $L$ describing its lowest-order density dependence. The bounds are found to be consistent with both recent calculations of the energies of pure neutron matter and constraints from nuclear experiments. These results are significant because many equations of state in active use for simulations of nuclear structure, heavy ion collisions, supernovae, neutron star mergers, and neutron star structure violate these constraints.

E. Kolomeitsev, J. Lattimer, A. Ohnishi, et. al.
Wed, 23 Nov 16
35/68

# Condensate of excitations in moving superfluids [CL]

A possibility of the condensation of excitations with a non-zero momentum in rectilinearly moving and rotating superfluid bosonic and fermionic (with Cooper pairing) media is considered in terms of a phenomenological order-parameter functional at zero and non-zero temperature. The results might be applicable to the description of bosonic systems like superfluid $^4$He, ultracold atomic Bose gases, charged pion and kaon condensates in rotating neutron stars, and various superconducting fermionic systems with pairing, like proton and color-superconducting components in compact stars, metallic superconductors, and neutral fermionic systems with pairing, like the neutron component in compact stars and ultracold atomic Fermi gases. Order parameters of the “mother” condensate in the superfluid and the new condensate of excitations, corresponding energy gains, critical temperatures and critical velocities are found.

E. Kolomeitsev and D. Voskresensky
Mon, 21 Nov 16
29/63

Comments: 15 pages, 1 figure reworked and extended version of arXiv:1501.00731 submitted to Prog. Theor Exp. Phys

# Microscopic Calculations of Vortex-Nucleus Interaction in the Neutron Star Crust [CL]

We investigate the dynamics of a quantized vortex and a nuclear impurity immersed in a neutron superfluid within a fully microscopic time-dependent three-dimensional approach. The magnitude and even the sign of the force between the quantized vortex and the nuclear impurity have been a matter of debate for over four decades. We determine that the vortex and the impurity repel at neutron densities, 0.014 fm$^{-3}$ and 0.031 fm$^{-3}$, which are relevant to the neutron star crust and the origin of glitches, while previous calculations have concluded that the force changes its sign between these two densities and predicted contradictory signs. The magnitude of the force increases with the density of neutron superfluid, while the magnitude of the pairing gap decreases in this density range.

K. Sekizawa, G. Wlazlowski, P. Magierski, et. al.
Wed, 14 Sep 16
58/75

Comments: 4 pages, 2 figures, Talk given at the 14th International Symposium on “Nuclei in the Cosmos” (NIC-XIV), June 19-24, 2016, Toki Messe, Niigata, Japan

# Ab initio and phenomenological studies of the static response of neutron matter [CL]

We investigate the problem of periodically modulated strongly interacting neutron matter. We carry out ab initio non-perturbative auxiliary-field diffusion Monte Carlo calculations using an external sinusoidal potential in addition to phenomenological two- and three-nucleon interactions. Several choices for the wave function ansatz are explored and special care is taken to extrapolate finite-sized results to the thermodynamic limit. We perform calculations at various densities as well as at different strengths and periodicities of the one-body potential. Our microscopic results are then used to constrain the isovector term from energy-density functional theories of nuclei at many different densities, while making sure to separate isovector contributions from bulk properties. Lastly, we use our results to extract the static density-density linear response function of neutron matter at different densities. Our findings provide insights into inhomogeneous neutron matter and are related to the physics of neutron-star crusts and neutron-rich nuclei.

M. Buraczynski and A. Gezerlis
Mon, 15 Aug 16
3/43

# Inflationary quasiparticle creation and thermalization dynamics in coupled Bose-Einstein condensates [CL]

A Bose gas in a double-well potential, exhibiting a true Bose-Einstein condensate (BEC) amplitude and initially performing Josephson oscillations, is a prototype of an isolated, non-equilibrium many-body system. We investigate the quasiparticle (QP) creation and thermalization dynamics of this system by solving the time-dependent Keldysh-Bogoliubov equations. We find avalanche-like QP creation due to a parametric resonance between BEC and QP oscillations, followed by slow, exponential relaxation to a thermal state at an elevated temperature, controlled by the initial excitation energy of the oscillating BEC above its ground state. The crossover between the two regimes occurs because of an effective decoupling of the QP and BEC oscillations. This dynamics is analogous to elementary particle creation in models of the early universe. The thermalization in our set-up occurs because the BEC acts as a grand canonical reservoir for the quasiparticle system.

A. Posazhennikova, M. Trujillo-Martinez and J. Kroha
Tue, 7 Jun 16
28/80

Comments: 5 pages, 4 Figures, final version accepted for publication in Phys. Rev. Lett

# Spectral splits of neutrinos as a BCS-BEC crossover type phenomenon [HEAP]

We show that the phenomenon of neutrino spectral split, which might be observed in the next galactic supernova neutrino signal, is analogous to the BCS-BEC crossover already observed in ultra cold atomic gas experiments. Although these two phenomena belong to two very different domains of physics, the propagation of neutrinos from highly interacting inner regions to the vacuum is reminiscent of the evolution of Cooper pairs between weak and strong interaction regimes. The Hamiltonians and the corresponding ground states undergo very similar transformations if one replaces the pair quasispin of the latter with the neutrino isospin of the former.

Y. Pehlivan, A. Subasi, N. Ghazanfari, et. al.
Tue, 22 Mar 16
59/72

# Equation of state of imbalanced cold matter from chiral perturbation theory [CL]

We study the thermodynamic properties of matter at vanishing temperature for non-extreme values of the isospin chemical potential and of the strange quark chemical potential. From the leading order pressure obtained by maximizing the static chiral Lagrangian density we derive a simple expression for the equation of state in the pion condensed phase and in the kaon condensed phase. We find an analytical expression for the maximum of the ratio between the chiral perturbation energy density and the Stefan-Boltzmann energy density as well as for the isospin chemical potential at the peak in good agreement with lattice simulations of quantum chromodynamics. We speculate on the location of the crossover from the Bose-Einstein condensate state to the Bardeen-Cooper-Schrieffer state by a simple analysis of the thermodynamic properties of the system. For $\mu_I \gtrsim 2 m_\pi$ the leading order chiral perturbation theory breaks down; as an example it underestimates the energy density of the system and leads to a wrong asymptotic behavior.

S. Carignano, A. Mammarella and M. Mannarelli
Thu, 4 Feb 16
11/50

# Static Response of Neutron Matter [CL]

We generalize the problem of strongly interacting neutron matter by adding a periodic external modulation. This allows us to study from first principles a neutron system that is extended and inhomogeneous, with connections to the physics of both neutron-star crusts and neutron-rich nuclei. We carry out fully non-perturbative microscopic Quantum Monte Carlo calculations of the energy of neutron matter at different densities, as well as different strengths and periodicities of the external potential. In order to remove systematic errors, we examine finite-size effects and the impact of the wave function ansatz. We also make contact with energy-density functional theories of nuclei and disentangle isovector gradient contributions from bulk properties. Finally, we calculate the static density-density linear response function of neutron matter and compare it with the response of other physical systems.

M. Buraczynski and A. Gezerlis
Fri, 23 Oct 15
25/63

# Instabilities in relativistic two-component (super)fluids [CL]

We study two-fluid systems with nonzero fluid velocities and compute their sound modes, which indicate various instabilities. For the case of two zero-temperature superfluids we employ a microscopic field-theoretical model of two coupled bosonic fields, including an entrainment coupling and a non-entrainment coupling. We analyse the onset of the various instabilities systematically and point out that the dynamical two-stream instability can only occur beyond Landau’s critical velocity, i.e., in an already energetically unstable regime. A qualitative difference is found for the case of two normal fluids, where certain transverse modes suffer a two-stream instability in an energetically stable regime if there is entrainment between the fluids. Since we work in a fully relativistic setup, our results are very general and of potential relevance for (super)fluids in neutron stars and, in the non-relativistic limit of our results, in the laboratory.

A. Haber, A. Schmitt and S. Stetina
Thu, 8 Oct 15
54/58

# Bose-Einstein condensates in neutron stars [CL]

In the two decades since the appearance of the book “Bose-Einstein Condensation” in 1995, there have been a number of developments in our understanding of dense matter. After a brief overview of neutron star structure and the Bose-Einstein condensed phases that have been proposed, we describe selected topics, including neutron and proton pairing gaps, the physics of the inner crust of neutron stars, where a neutron fluid penetrates a lattice of nuclei, meson condensates, and pairing in dense quark matter. Especial emphasis is placed on basic physical effects and on connections to the physics of cold atomic gases.

C. Pethick, T. Schaefer and A. Schwenk
Wed, 22 Jul 15
1/59

Comments: 22 pages, 2 figures, to appear in “Universal Themes of Bose-Einstein Condensation”, edited by D.W. Snoke, N.P. Proukakis and P.B. Littlewood (Cambridge University Press)

# Phase ordering percolation and domain-wall survival in segregating binary Bose-Einstein condensates [CL]

Percolation theory is applied to the phase transition dynamics of domain pattern formation in segregating quasi-two-dimensional binary Bose–Einstein condensates. Our numerical experiments revealed that the percolation threshold is close to 0.5. A long-range open domain wall appears with a fractal dimension between two percolating domains. Such a wall can survive for a long time as a relic of the phase transition according to the dynamic finite-size-scaling hypothesis, which seems to be in contrast to the current understanding in cosmology that an infinite defect violates a scale invariance.

H. Takeuchi, Y. Mizuno and K. Dehara
Tue, 12 May 15
3/77

# Multiple Period States of the Superfluid Fermi Gas in an Optical Lattice [CL]

We study multiple period states of a superfluid Fermi gas in an optical lattice along the Bardeen-Cooper-Schrieffer (BCS) to Bose-Einstein condensate (BEC) crossover. The existence of states whose period is a multiple of the lattice spacing is a consequence of the non-linear behavior of the gas, which is due to the presence of the order parameter associated with superfluidity. By solving Bogoliubov-de Gennes equations we find that, in the BCS side of the crossover, the multiple period states can be energetically favorable compared to the normal Bloch states and their survival time against dynamical instability drastically increases, suggesting that these states can be accessible in current experiments with ultracold gases. This is in sharp contrast to the situation in BECs.

S. Yoon, F. Dalfovo, T. Nakatsukasa, et. al.
Mon, 30 Mar 15
40/65

# Neutron Matter from Low to High Density [CL]

Neutron matter is an intriguing nuclear system with multiple connections to other areas of physics. Considerable progress has been made over the last two decades in exploring the properties of pure neutron fluids. Here we begin by reviewing work done to explore the behavior of very low density neutron matter, which forms a strongly paired superfluid and is thus similar to cold Fermi atoms, though at energy scales differing by many orders of magnitude. We then increase the density, discussing work that ties the study of neutron matter with the determination of the properties of neutron-rich nuclei and neutron-star crusts. After this, we review the impact neutron matter at even higher densities has on the mass-radius relation of neutron stars, thereby making contact with astrophysical observations.

S. Gandolfi, A. Gezerlis and J. Carlson
Mon, 26 Jan 15
40/46

Comments: 30 pages, 11 figures; prepared for Annual Review of Nuclear and Particle Science

# Quantum Monte Carlo methods for nuclear physics [CL]

Quantum Monte Carlo methods have proved very valuable to study the structure and reactions of light nuclei and nucleonic matter starting from realistic nuclear interactions and currents. These ab-initio calculations reproduce many low-lying states and transition moments in light nuclei, and simultaneously predict many properties of light nuclei and neutron matter over a rather wide range of energy and momenta. We review the nuclear interactions and currents, and describe the continuum Quantum Monte Carlo methods used in nuclear physics. These methods are similar to those used in condensed matter and electronic structure but naturally include spin-isospin, tensor, spin-orbit, and three-body interactions. We present a variety of results including the low-lying spectra of light nuclei, nuclear form factors, and transition matrix elements. We also describe low-energy scattering techniques, studies of the electroweak response of nuclei relevant in electron and neutrino scattering, and the properties of dense nucleonic matter as found in neutron stars. A coherent picture of nuclear structure and dynamics emerges based upon rather simple but realistic interactions and currents.

J. Carlson, S. Gandolfi, F. Pederiva, et. al.
Wed, 10 Dec 14
30/61

Comments: 53 pages, 38 figures, review article

# BCS-BEC crossovers and unconventional phases in dilute nuclear matter. II [CL]

We study the phase diagram of isospin-asymmetrical nuclear matter in the density-temperature plane, allowing for four competing phases of nuclear matter: (i) the unpaired phase, (ii) the translationally and rotationally symmetric, but isospin-asymmetrical BCS condensate, (iii) the current-carrying Larkin-Ovchinnikov-Fulde-Ferrell phase, and (iv) the heterogeneous phase-separated phase. The phase diagram of nuclear matter composed of these phases features two tri-critical points in general, as well as crossovers from the asymmetrical BCS phase to a BEC of deuterons plus a neutron gas, both for the homogeneous superfluid phase (at high temperatures) and for the heterogeneous phase (at low temperatures). The BCS-BEC type crossover in the condensate occurs as the density is reduced. We analyze in detail some intrinsic properties of these phases, including the Cooper-pair wave function, the coherence length, the occupation numbers of majority and minority nucleonic components, and the dispersion relations of quasiparticle excitations about the ground state. We show by explicit examples that the physics of the individual phases and the transition from weak to strong coupling can be well understood by tracing the behavior of these quantities.

M. Stein, A. Sedrakian, X. Huang, et. al.
Tue, 7 Oct 14
60/69

Comments: 14 pages, 16 figures, uses RevTex 4

# Doppler Shift of de Broglie Waves- Black body System of Fermions and Massive Bosons [CL]

The Doppler shift of de Broglie wave is obtained for fermions and massive bosons in a many body Fermi gas or in a Bose gas using the Lorentz transformations for momentum and energy of the particles. A formalism is developed to obtain the variation of de Broglie waves with temperature using the classic idea of Wien. It has been noticed that unlike the photon gas or electromagnetic waves in a black body chamber, where the variation is determined by the Wien’s displacement law, for Fermi gas the de Borglie wavelength increases with temperature and at a critical temperature it becomes infinity. This is the quantum to classical transition temperature for fermions. On the other hand for bosons, the de Broglie wavelength decreases with the increase in temperature. There is a minimum possible temperature at which condensation takes place. At the minimum of thr temperature the de Broglie wavelength of bosons become infinitely large. Unlike a transition from quantum to classical world this is indirectly related to the large value of coherence length for the bosons in the condensed phase.

S. De and S. Chakrabarty
Fri, 29 Aug 14
48/51

Comments: Five pages REVTEX file, no figures

# Pairing and superfluidity of nucleons in neutron stars [CL]

We survey the current status of understanding of pairing and superfluidity of neutrons and protons in neutron stars from a theoretical perspective, with emphasis on basic physical properties. During the past two decades, the blossoming of the field of ultracold atomic gases and the development of quantum Monte Carlo methods for solving the many-body problem have been two important sources of inspiration, and we shall describe how these have given insight into neutron pairing gaps. The equilibrium properties and collective oscillations of the inner crust of neutron stars, where neutrons paired in a $^1$S$_0$ state coexist with a lattice of neutron-rich nuclei, are also described. While pairing gaps are well understood at densities less than one tenth of the nuclear saturation density, significant uncertainties exist at higher densities due to the complicated nature of nucleon-nucleon interactions, the difficulty of solving the many-body problem under these conditions, and the increasing importance of many-nucleon interactions. We also touch more briefly on the subject of pairing of neutrons in other angular momentum states, specifically the $^3$P$_2$ state, as well as pairing of protons.

A. Gezerlis, C. Pethick and A. Schwenk
Wed, 25 Jun 14
64/67

Comments: 48 pages, 13 figures; chapter in “Novel Superfluids, Volume 2”, edited by K. H. Bennemann and J. B. Ketterson (Oxford University Press)

# A theory of finite-temperature Bose-Einstein condensates in neutron stars [CL]

We investigate the possible occurrence of a Bose-Einstein condensed phase of matter within neutron stars due to the formation of Cooper pairs among the superfluid neutrons. To this end we study the condensation of bosonic particles under the influence of both a short-range contact and a long-range gravitational interaction in the framework of a Hartree-Fock theory. We consider a finite-temperature scenario, generalizing existing approaches, and derive macroscopic and astrophysically relevant quantities like a mass limit for neutron stars.

C. Gruber and A. Pelster
Tue, 18 Mar 14
21/62

# Quantum Monte Carlo calculations of neutron matter with non-local chiral interactions [CL]

We present fully non-perturbative quantum Monte Carlo calculations with non-local chiral effective field theory (EFT) interactions for the ground state properties of neutron matter. The equation of state, the nucleon chemical potentials and the momentum distribution in pure neutron matter up to one and a half times the nuclear saturation density are computed with a newly optimized chiral EFT interaction at next-to-next-to-leading order. This work opens the way to systematic order by order benchmarking of chiral EFT interactions, and \emph{ab initio} prediction of nuclear properties while respecting the symmetries of quantum chromodynamics.

A. Roggero, A. Mukherjee and F. Pederiva
Mon, 10 Feb 14
38/49

# Self-gravitating Bose-Einstein condensates and the Thomas-Fermi approximation [CL]

Self-gravitating Bose-Einstein condensates have been proposed in various astrophysical contexts, including Bose-stars and BEC dark matter halos. These systems are described by a combination of the Gross-Pitaevskii and Poisson equations (the GPP system). In the analysis of these hypothetical objects, the Thomas-Fermi (TF) approximation is widely used. This approximation is based on the assumption that in the presence of a large number of particles, the kinetic term in the Gross-Pitaevskii energy functional can be neglected, yet this assumption is violated near the condensate surface. We also show that the total energy of the self-gravitating condensate in the TF-approximation is positive. The stability of a self-gravitating system is dependent on the total energy being negative. Therefore, the TF approximation is ill suited to formulate initial conditions in numerical simulations. As an alternative, we offer an approximate solution of the full GPP system.

Wed, 5 Feb 14
41/61

# The amazing properties of crystalline color superconductors [CL]

This paper is a brief journey into the amazing realm of crystalline color superconductors. Starting from a qualitative description of superfluids, superconductors and supersolids, we show how inhomogeneous phases may arise when the system is under stress. These basic concepts are then extended to quark matter, in which a richer variety of phases can be realized. Then, the most interesting properties of the crystalline color superconductors are presented. This brief journey ends with a discussion of crystalline color superconductors in compact stars and related astrophysical observables. We aim at providing a pedagogical introduction for nonexpert in the field to a few interesting properties of crystalline color superconductors, without discussing the methods and the technicalities. Thus, the results are presented without a proof. However, we try to give a qualitatively clear description of the main concepts, using standard quantum field theory and analogies with condensed matter systems.

Thu, 30 Jan 14
9/59