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The planar Thirring model is thought to have a strongly coupled critical point for a single flavor of fermion. We look at the calculation of the bilinear condensate in this critical region, and its characterization via an equation of state. Since the computation is numerically challenging, we investigate the improved Dirac operators. We present findings on different methods of calculation using a rational hybrid Monte-Carlo scheme, and calculations of the bilinear condensate, an equation of state and the associated critical exponents. Overlap and domain wall Dirac operators, and variants therein are considered.

In this paper, we consider the Casfimir effect in a (1+1)-dimensional model with a critical mode. Such a mode gives rise to a condensate described by the nonlinear Gross–Pitaevskii equation. In the condensate, there are two sources of the Casimir force; one is the conventional one resulting from the fluctuations, the other follows from the condensate. We consider three simple models that allow for condensate solutions in terms of elliptic Jacobi functions. We also investigate a method for obtaining approximate solutions and show its range of applicability. In all three examples, we compute the condensate energy. In one example with a finite interval with Robin boundary conditions on one side and Dirichlet conditions on the other side, we calculate the vacuum energy and the Casimir force. There is a competition between the forces from the condensate and the fluctuations. We mention that the force from the condensate is always repulsive.

We consider a mean-field model to describe the dynamics of $N_1$ bosons of species one and $N_2$ bosons of species two in the limit as $N_1$ and $N_2$ go to infinity. We embed this model into Fock space and use it to describe the time evolution of coherent states which represent two-component condensates. Following this approach, we obtain a microscopic quantum description for the dynamics of such systems, determined by the Schrödinger equation. Associated to the solution to the Schrödinger equation, we have a reduced density operator for one particle in the first component of the condensate and one particle in the second component. In this paper, we estimate the difference between this operator and the projection onto the tensor product of two functions that are solutions of a system of equations of Hartree type. Our results show that this difference goes to zero as $N_1$ and $N_2$ go to infinity.

We consider a model of interacting cosmological constant/quintessence, where dark matter and dark energy behave as, respectively, two coexisting phases of a fluid, a thermally excited Bose component and a condensate, respectively. In a simple phenomenological model for the dark components interaction we find that their energy density evolution is strongly coupled during the universe evolution. This feature provides a possible way out for the coincidence problem affecting many quintessence models.

There has been a discrepancy between values of the pion-nucleon sigma term extracted by two different methods for many years. Analysis of recent high precision pion-nucleon data has widened the gap between the two determinations. It is argued that the two extractions correspond to different quantities and that the difference between them can be understood and calculated.

An application of the quantum N-portrait to the Universe is discussed, wherein the spacetime geometry is understood as a Bose–Einstein condensate of N soft gravitons. If near or at the critical point of a quantum phase transition, indications are found that the vacuum energy is partly suppressed by 1/N, as being due to quanta not in the condensate state. Time evolution decreases this suppression, which might have implications for cosmic expansion.

We present the Higgs mechanism in the context of the EW-scale ${\nu }_R$ model in which electroweak symmetry is dynamically broken by condensates of mirror quark and right-handed neutrino through the exchange of one fundamental Higgs doublet and one fundamental Higgs triplet, respectively. The formation of these condensates is dynamically investigated by using the Schwinger–Dyson approach. The occurrence of these condensates will give rise to the rich Higgs spectrum. In addition, the VEVs of Higgs fields is also discussed in this dynamical phenomenon.

For a class of algebras, denote by Con_c the class of all (∨, 0)-semilattices isomorphic to the semilattice Con_cA of all compact congruences of A, for some A in . For classes and of algebras, we denote by the smallest cardinality of a (∨, 0)-semilattices in Con_c which is not in Con_c if it exists, ∞ otherwise. We prove a general theorem, with categorical flavor, that implies that for all finitely generated congruence-distributive varieties and , is either finite, or ℵ_n for some natural number n, or ∞. We also find two finitely generated modular lattice varieties and such that , thus answering a question by J. Tůma and F. Wehrung.

In this work we discuss points of interest for a general phase diagram of nuclear matter at alternative conditions (such as isospin broken phase and existence of anti-matter state(s)) which are relevant for the description of astrophysics. The inclusion of light isovector spin zero mesons in relativistic models of nuclear systems is discussed and deviation from the usual results for the symmetry energy description is found in agreement with a development done for a non-relativistic description of nuclear matter.

This paper studies the quark condensate, magnetic moment, magnetic polarization, and magnetic susceptibility in a strong external magnetic field by employing the Dyson–Schwinger equations (DSE). The results show these physical quantities as functions of the magnetic field. We note that the quark’s spin polarizations are approximately proportional to the magnetic field magnitude. For comparison, we investigate the magnetic moments and susceptibility of the nucleon in the constituent quark model framework and demonstrate that both these quantities increase as the magnetic field rises.

Anti-elementarity is a strong way of ensuring that a class of structures, in a given first-order language, is not closed under elementary equivalence with respect to any infinitary language of the form ${ℒ}_{\infty \lambda }$. We prove that many naturally defined classes are anti-elementary, including the following:

• the class of all lattices of finitely generated convex $\ell$-subgroups of members of any class of $\ell$-groups containing all Archimedean $\ell$-groups;
• the class of all semilattices of finitely generated $\ell$-ideals of members of any nontrivial quasivariety of $\ell$-groups;
• the class of all Stone duals of spectra of MV-algebras — this yields a negative solution to the MV-spectrum Problem;
• the class of all semilattices of finitely generated two-sided ideals of rings;
• the class of all semilattices of finitely generated submodules of modules;
• the class of all monoids encoding the nonstable K₀-theory of von Neumann regular rings, respectively, C*-algebras of real rank zero;
• (assuming arbitrarily large Erdős cardinals) the class of all coordinatizable sectionally complemented modular lattices with a large $4$-frame.

The main underlying principle is that under quite general conditions, for a functor $\mathrm{\Phi }:{𝒜}\to {ℬ}$, if there exists a noncommutative diagram $\overrightarrow{D}$ of ${𝒜}$, indexed by a common sort of poset called an almost join-semilattice, such that

• $\mathrm{\Phi }{\overrightarrow{D}}^I$ is a commutative diagram for every set $I$,
• $\mathrm{\Phi }\overrightarrow{D}\ncong \mathrm{\Phi }\overrightarrow{X}$ for any commutative diagram $\overrightarrow{X}$ in ${𝒜}$,

then the range of $\mathrm{\Phi }$ is anti-elementary.

The fermionic condensate and current density are investigated in a (2 + 1)-dimensional conical spacetime in the presence of a circular boundary and a magnetic flux. On the boundary the fermionic field obeys the MIT bag boundary condition. For irregular modes, we consider a special case of boundary conditions at the cone apex, when the MIT bag boundary condition is imposed at a finite radius, which is then taken to zero. The condensate and current are periodic functions of the magnetic flux with the period equal to the flux quantum. For both exterior and interior regions, the expectation values are decomposed into boundary-free and boundary-induced parts. In the case of a massless field the boundary-free part in the vacuum expectation value of the charge density vanishes, whereas the presence of the boundary induces nonzero charge density. At distances from the boundary larger than the Compton wavelength of the fermion particle, the condensate and current decay exponentially, with the decay rate depending on the opening angle of the cone.

We construct an effective field theory for a condensate of cold Fermi atoms whose scattering is controlled by a Feshbach resonance, with particular emphasis on the speed of sound and its hydrodynamic description.

The dynamical Maxwell-cut, a degeneracy is shown to be a precursor of condensate in the ɸ⁴ and the sine-Gordon models. The difference of the way the Maxwell-cut is obtained is pointed out and quantum censorship, the generation of semiclassically looking phenomenon by loop-corrections is conjectured in the sine-Gordon model. It is argued that quantum censorship and gluon confinement exclude each other.