Triangular Gross-Pitaevskii breathers and Damski-Chandrasekhar shock waves

The recently proposed map [5] between the hydrodynamic equations governing the two-dimensional triangular cold-bosonic breathers [1] and the high-density zero-temperature triangular free-fermionic clouds, both trapped harmonically, perfectly explains the former phenomenon but leaves uninterpreted the nature of the initial (t=0) singularity. This singularity is a density discontinuity that leads, in the bosonic case, to an infinite force at the cloud edge. The map itself becomes invalid at times t<0t<0. A similar singularity appears at t = T/4t=T/4, where T is the period of the harmonic trap, with the Fermi-Bose map becoming invalid at t > T/4t>T/4. Here, we first map—using the scale invariance of the problem—the trapped motion to an untrapped one. Then we show that in the new representation, the solution [5] becomes, along a ray in the direction normal to one of the three edges of the initial cloud, a freely propagating one-dimensional shock wave of a class proposed by Damski in [7]. There, for a broad class of initial conditions, the one-dimensional hydrodynamic equations can be mapped to the inviscid Burgers’ equation, which is equivalent to a nonlinear transport equation. More specifically, under the Damski map, the t=0 singularity of the original problem becomes, verbatim, the initial condition for the wave catastrophe solution found by Chandrasekhar in 1943 [9]. At t=T/8t=T/8, our interpretation ceases to exist: at this instance, all three effectively one-dimensional shock waves emanating from each of the three sides of the initial triangle collide at the origin, and the 2D-1D correspondence between the solution of [5] and the Damski-Chandrasekhar shock wave becomes invalid.

Parafermion theory from the q-deformed algebra with q a root of unity

In this paper, we find the [Formula: see text]-deformed algebra with the finite- and infinite-dimensional Fock space and both the fermionic limit and the bosonic limit. Using the cardinality of set theory, we propose the Hamiltonian interpolating bosonic case and fermionic case, which enables us to construct the proper partition function and internal energy. As examples, we discuss the specific heat of free [Formula: see text] parafermion gas model and [Formula: see text] parafermion star.

Two component boson–fermion plasma at finite temperature

We discuss thermodynamic stability of neutral real (quantum) matter from the point of view of a computer experiment at finite, nonzero, temperature. We perform (restricted) path integral Monte Carlo simulations of the two component plasma where the two species are both bosons, both fermions, and one boson and one fermion. We calculate the structure of the plasma and discuss about the formation of binded couples of oppositely charged particles. The purely bosonic case is thermodynamically unstable. In this case we find an undetermined size-dependent contact value unlike partial radial distribution function. For the purely fermionic case, we find a demixing transition with binding also of like species.

STABILITY FOR A SYSTEM OF N FERMIONS PLUS A DIFFERENT PARTICLE WITH ZERO-RANGE INTERACTIONS

We study the stability problem for a non-relativistic quantum system in dimension three composed by N ≥ 2 identical fermions, with unit mass, interacting with a different particle, with mass m, via a zero-range interaction of strength α ∈ ℝ. We construct the corresponding renormalized quadratic (or energy) form [Formula: see text] and the so-called Skornyakov–Ter–Martirosyan symmetric extension Hα, which is the natural candidate as Hamiltonian of the system. We find a value of the mass m*(N) such that for m > m*(N) the form [Formula: see text] is closed and bounded from below. As a consequence, [Formula: see text] defines a unique self-adjoint and bounded from below extension of Hα and therefore the system is stable. On the other hand, we also show that the form [Formula: see text] is unbounded from below for m < m*(2). In analogy with the well-known bosonic case, this suggests that the system is unstable for m < m*(2) and the so-called Thomas effect occurs.

Quantum entanglement of Dirac field in background of an asymptotically flat static black hole

The entanglement of the Dirac field in the asymptotically flat black hole is investigated. Unlike the bosonic case in which the initial entanglement vanishes in the limit of infinite Hawking temperature, in this case the entanglement achieves a nonvanishing minimum values, which shows that the entanglement is never completely destroyed when black hole evaporates completely. Another interesting result is that the mutual information in this limit equals to just half of its own initial value, which may be an universal property for any fields.

INVARIANCE OF WEYL ORDERING OF FERMI OPERATORS UNDER SIMILAR TRANSFORMATIONS

A Weyl–Wigner quantization scheme for Fermi system which is parallel to the bosonic case is established. We prove a new theorem: Weyl ordering of Fermi operators is invariant under fermionic similar transformations. Comparing with the preceding paper,1 we see the Bose–Fermi supersymmetry in this aspect. As an application of the theorem, we construct a generalized fermionic squeezed state.

N = 1, 2 SUPER-NLS HIERARCHIES AS SUPER-KP COSET REDUCTIONS

We define consistent finite-superfield reductions of the N = 1, 2 super-KP hierarchies via the coset approach we have already developed for reducing the bosonic KP hierarchy [generating for example the NLS hierarchy from the [Formula: see text] coset]. We work in a manifestly supersymmetric framework and illustrate our method by treating explicitly the N = 1, 2 super-NLS hierarchies. With respect to the bosonic case the ordinary covariant derivative is now replaced by a spinorial one which contains a spin-[Formula: see text] superfield. Each coset reduction is associated with a rational super-[Formula: see text] algebra encoding a nonlinear super-[Formula: see text]-algebra structure. In the N = 2 case two conjugate sets of super-Lax operators, equations of motion and infinite Hamiltonians in involution are derived. Modified hierarchies are obtained from the original ones via free-field mappings [just as an m-NLS equation arises from representing the [Formula: see text] algebra through the classical Wakimoto free fields].