Soliton trains in Bose-Fermi mixtures

We theoretically consider the formation of bright solitons in a mixture of Bose and Fermi degenerate gases. While we assume the forces between atoms in a pure Bose component to be effectively repulsive, their character can be changed from repulsive to attractive in the presence of fermions provided the Bose and Fermi gases attract each other strongly enough. In such a regime the Bose component becomes a gas of effectively attractive atoms. Hence, generating bright solitons in the bosonic gas is possible. Indeed, after a sudden increase of the strength of attraction between bosons and fermions (realized by using a Feshbach resonance technique or by firm radial squeezing of both samples) soliton trains appear in the Bose-Fermi mixture.     

Mixtures of correlated bosons and fermions: Dynamical mean‐field theory for normal and condensed phases

We derive a dynamical mean‐field theory for mixtures of interacting bosons and fermions on a lattice (BF‐DMFT). The BF‐DMFT is a comprehensive, thermodynamically consistent framework for the theoretical investigation of Bose‐Fermi mixtures and is applicable for arbitrary values of the coupling parameters and temperatures. It becomes exact in the limit of high spatial dimensions d or coordination number Z of the lattice. In particular, the BF‐DMFT treats normal and condensed bosons on equal footing and thus includes the effects caused by their dynamic coupling. Using the BF‐DMFT we investigate two different interaction models of correlated lattice bosons and fermions, one where all particles are spinless (model I) and one where fermions carry a spin one‐half (model II). In model I the local, repulsive interaction between bosons and fermions can give rise to an attractive effective interaction between the bosons. In model II it can also lead to an attraction between the fermions.     

Bosonic and fermionic dipoles on a ring

We show that dipolar bosons and fermions confined in a quasi-one-dimensional ring trap exhibit a rich variety of states because their interaction is inhomogeneous. For purely repulsive interactions, with increasing strength of the dipolar coupling there is a crossover from a gaslike state to an inhomogeneous crystal-like one. For small enough angles between the dipoles and the plane of the ring, there are regions with attractive interactions, and clustered states can form.     

Coherence properties of two trapped particles

We analyse the coherence properties of two particles trapped in a one-dimensional harmonic potential. This simple model allows us to derive analytic expressions for the first and second order coherence functions. We investigate their properties depending on the particle nature and the temperature of the quantum gas. We find that at zero temperature non-interacting bosons and fermions show very different correlations, while they coincide for higher temperatures. We observe atom bunching for bosons and atom anti-bunching for fermions. When the effect of s-wave scattering between bosons is taken into account, we find that the range of coherence is enhanced or reduced for repulsive or attractive potentials, respectively. Strongly repelling bosons become in some way more “fermion-like" and show anti-bunching. Their first order coherence function, however, differs from that for fermions. Received 19 September 2002 Published online 4 February 2003     

Exact solutions of a one-dimensional mixture of spinor bosons and spinor fermions

The exact solutions of a one-dimensional mixture of spinor bosons and spinor fermions with δ-function interactions are studied. Some new sets of Bethe ansatz equations are obtained by using the graded nest quantum inverse scattering method. Many interesting features appear in the system. For example, the wave function has the SU(2|2) supersymmetry. It is also found that the ground state of the system is partial polarized, where the fermions form a spin singlet state and the bosons are totally polarized. From the solution of Bethe ansatz equations, it is shown that all the momentum, spin and isospin rapidities at the ground state are real if the interactions between the particles are repulsive; while the fermions form two-particle bounded states and the bosons form one large bound state, which means the bosons condensed at the zero momentum point, if the interactions are attractive. The charge, spin and isospin excitations are discussed in detail. The thermodynamic Bethe ansatz equations are also derived and their solutions at some special cases are obtained analytically.     

Fermions coupled to autonomous (λΦ 4)3+1 theory

Recent Gaussian-effective-potential results for “autonomous”λΦ ⁴ theory, an apparently nontrivial, positive-λ, 3+1 dimensional theory, are extended to include a Yukawa coupling to fermions. The formerly massless bosons of the symmetric phase acquire a mass.     

Role of quantum statistics in multi-particle decay dynamics

The role of quantum statistics in the decay dynamics of a multi-particle state, which is suddenly released from a confining potential, is investigated. For an initially confined double particle state, the exact dynamics is presented for both bosons and fermions. The time-evolution of the probability to measure two-particle is evaluated and some counterintuitive features are discussed. For instance, it is shown that although there is a higher chance of finding the two bosons (as oppose to fermions, and even distinguishable particles) at the initial trap region, there is a higher chance (higher than fermions) of finding them on two opposite sides of the trap as if the repulsion between bosons is higher than the repulsion between fermions. The results are demonstrated by numerical simulations and are calculated analytically in the short-time approximation. Furthermore, experimental validation is suggested.     

Repulsive bubble–bubble interaction in ultrasonic field

The bubble–bubble interaction(BBI) is attractive in most cases, but also could be repulsive. In the present study,three specific mechanisms of repulsive BBI are given. The great contribution to the repulsive BBI is derived from the large radius of the bubble catching the rebound point of the other bubble. For "elastic" bubble and "inelastic" bubble, with the increase of the phase shift between two bubbles, the BBI changes from attractive to repulsive, and the repulsion can be maintained. For both "elastic" bubbles, the BBI alternates between attractive interaction and repulsive interaction along the direction where the ambient radius of one of bubbles increases. For stimulating bubble and stimulated bubble, the BBI can be repulsive. Its property depends on the ambient radii of bubbles. In addition, the distribution of the radiation forces in ambient radius space shows that the BBI is sensitive to the size of bubble and is complex because the bubbles are not of the same size in an ultrasonic field. Finally, as the distance increases or decreases monotonically with time, the absolute value of the BBI decreases or increases, correspondingly. The BBI can oscillate not only in strength but also in polarity when the distance fluctuates with time.     

Auxiliary field Monte-Carlo for quantum many-body ground states

We develop an algorithm for determining the exact ground state properties of quantum many-body systems which is equally applicable to bosons and fermions. The Schroedinger eigenvalue equation for the ground state energy is recast as a many-dimensional integral using the Hubbard-Stratonovitch representation of the imaginary-time many-body evolution operator. The integral is then evaluated stochastically. We test the algorithm for an exactly soluble boson system with an attractive potential and then extend it to fermions and repulsive potentials. Importance sampling is crucial to the success of the method, particularly for more complex systems. Computational efficiency is improved by performing the calculations in Fourier space.     

Composite fermions,trios, and quartets in the Fermi-Bose mixture of neutral particles

We consider the model of a Fermi-Bose mixture with strong hard-core repulsion between particles of the same sort and attraction between particles of different sorts. In this case, in addition to the standard anomalous averages of the type 〈b〉, 〈bb〉, and 〈cc〉, pairing between fermions and bosons of the type 〈bc〉 is possible. This pairing corresponds to creation of composite fermions in the system. At low temperatures and equal densities of fermions and bosons, composite fermions are further paired into quartets. At higher temperatures, trios consisting of composite fermions and elementary bosons are also present in the system. Our investigations are important in connection with the recent observation of weakly bound dimers in magnetic and optical dipole traps at ultralow temperatures and with the observation of collapse of a Fermi gas in an attractive Fermi-Bose mixture of neutral particles.     

Vectorial versus axial Goldstone bosons

The Yukawa interactions of fermions with Goldstone bosons are given in closed form for an arbitrary renormalizable field theory to all orders of perturbation theory or for a general effective Lagrangian. Although the diagonal couplings are always pseudoscalar there is an important difference between spontaneously broken vector and axial-vector global symmetries. Compared to the axial case, the diagonal couplings of “vectorial” Goldstone bosons to charged fermions are suppressed by mixing angles or appear only via radiative corrections involving gauge fields. This general result may be relevant for the problem of flavour symmetry breaking in composite models.     

Class of exactly solvable pairing models

We present three classes of exactly solvable models for fermion and boson systems, based on the pairing interaction. These models are solvable in any dimension. As an example we show the first results for fermions interacting with repulsive pairing forces in a two-dimensional square lattice. In spite of the repulsive pairing force the exact results show attractive pair correlations.     

Do Bosons Condense in a Homogeneous Magnetic Field?

It has been known since the paper⁽²⁶⁾ and then due to a rigorous result⁽³⁾ that the answer to the question in the title is negative for a three-dimensional “ideal gas of charged bosons”. The present paper adds a new rigorous result in this direction. We show that the answer to the question becomes positive, if this “ideal gas of charged bosons” is simultaneously embedded in an appropriate periodic external potential. We prove that it is true for the Perfect Bose Gas (PBG), as well as for the Imperfect Bose Gas with a Mean-Field repulsive particle interaction.     

Spin and statistics of quantum kinks

Apart from some brief and inconclusive remarks concerning the problem of spin and statistics of quantum kinks in space-time dimension D > 2, we give a detailed discussion of the D = 2 situation. Our main results is that two-dimensional quantum kinks are statistical “schizons”; they exist in the same Hilbert space either as bosons or as fermions. In those cases where one can introduce local kink-sector generating operators as in the sine-Gordon model, the Bose and Fermi fields are strictly local fields, which are relatively non-local with respect to each other.     

The solution of the quantum mechanical many-body problem bound by harmonic forces as a translationally invariant basis for nuclear structure calculations

A very simple method to obtain the translationally invariant wave functions of anA-particle system of bosons or fermions bound by harmonic forces is derived and a formalism to apply these solutions as a basis for nuclear structure calculations is presented. The simplicity of this formalism is demonstrated for⁴He. The method is not restricted toA≦4.     

Universal vortex formation in rotating traps with bosons and fermions

We show that the rotation of trapped quantum mechanical particles with a repulsive interaction can lead to vortex formation, irrespective of whether the particles are bosons or (unpaired) fermions. The exact many-particle wave function constitutes similar structures in both cases, implying that this vortex formation is indeed universal.     

Search for elementary quantum statistics

Bose-Einstein and Fermi-Dirac are the main quantum statistics. Therefore, it is likely that if truly elementary building blocks of Nature exist, they are either bosons or fermions, so that it is also likely that one, and only one, of the following possibilities, concerning those elementary building blocks, is correct: (i) all of them are fermions; (ii) some of them are bosons, others fermions; (iii) all of them are bosons; (iv) the distinction between these cases is methodological, not physical. Since tensors can be constructed from spinors, most physicists support one of the first two points of view. However, by starting from the fact that now it is known that bosonization makes sense, and developing a former research by Penney, we defend the point of view that, at least in a finite model of the Universe, the third point of view is the more likely. To avoid confusion we state that we are not concerned with the whole set of the so-called “elementary particles” since most physicists believe by now that, e.g., hadrons are built from quarks, nor concerned with quarks since many physicists suspect they are also composite objects. This research concerns the true elementary building blocks of Nature, assuming that such set exists, whatever those building blocks are. Finally, we extend this research to general finite associative algebras, enlarging the physical applicability of our point of view concerning the role of bosons in Nature.