Nonassociative Weyl star products

Deformation quantization is a formal deformation of the algebra of smooth functions on some manifold. In the classical setting, the Poisson bracket serves as an initial conditions, while the associativity allows to proceed to higher orders. Some applications to string theory require deformation in the direction of a quasi-Poisson bracket (that does not satisfy the Jacobi identity). This initial condition is incompatible with associativity, it is quite unclear which restrictions can be imposed on the deformation. We show that for any quasi-Poisson bracket the deformation quantization exists and is essentially unique if one requires (weak) hermiticity and the Weyl condition. We also propose an iterative procedure that allows to compute the star product up to any desired order.Comment: discussion extended, tipos corrected, published versio

Two-body relaxation of spin-polarized fermions in reduced dimensionalities near a p-wave Feshbach resonance

We study inelastic two-body relaxation in a spin-polarized ultracold Fermi gas in the presence of a p-wave Feshbach resonance. It is shown that in reduced dimensionalities, especially in the quasi-one-dimensional case, the enhancement of the inelastic rate constant on approach to the resonance is strongly suppressed compared to three dimensions. This may open promising paths for obtaining novel many-body states.Comment: 14 pages, 12 figure

Non-Markovian dynamics with fermions

Employing the quadratic fermionic Hamiltonians for the collective and internal subsystems with a linear coupling, we studied the role of fermionic statistics on the dynamics of the collective motion. The transport coefficients are discussed as well as the associated fluctuation-dissipation relation. Due to different nature of the particles, the path to equilibrium is slightly affected. However, in the weak coupling regime, the time-scale for approaching equilibrium is found to be globally unchanged. The Pauli-blocking effect can modify the usual picture in open quantum system. In some limits, contrary to boson, this effect can strongly hinder the influence of the bath by blocking the interacting channels.Comment: 13 pages, 6 figures. Submitted to PR

Neutron pair transfer in sub-barrier capture process

The sub-barrier capture reactions following the neutron pair transfer are proposed to be used for the indirect study of neutron-neutron correlation in the surface region of nucleus. The strong effect of the dineutron-like clusters transfer stemming from the surface of magic and non-magic nuclei $^{18}$O, $^{48}$Ca, $^{64}$Ni, $^{94,96}$Mo, $^{100,102,104}$Ru, $^{104,106,108}$Pd, and $^{112,114,116,118,120,124,132}$Sn is demonstrated. The dominance of two-neutron transfer channel at the vicinity of the Coulomb barrier is further supported by time-dependent mean-field approaches.Comment: 17 pages, 7 figures, accepted in PR

Spaceability in Banach and quasi-Banach sequence spaces

Let $X$ be a Banach space. We prove that, for a large class of Banach or quasi-Banach spaces $E$ of $X$-valued sequences, the sets $E-\bigcup _{q\in\Gamma}\ell_{q}(X)$, where $\Gamma$ is any subset of $(0,\infty]$, and $E-c_{0}(X)$ contain closed infinite-dimensional subspaces of $E$ (if non-empty, of course). This result is applied in several particular cases and it is also shown that the same technique can be used to improve a result on the existence of spaces formed by norm-attaining linear operators.Comment: 9 page

On perturbations of the isometric semigroup of shifts on the semiaxis

We study perturbations $(\tilde\tau_t)_{t\ge 0}$ of the semigroup of shifts $(\tau_t)_{t\ge 0}$ on $L^2(\R_+)$ with the property that $\tilde\tau_t - \tau_t$ belongs to a certain Schatten-von Neumann class \gS_p with $p\ge 1$. We show that, for the unitary component in the Wold-Kolmogorov decomposition of the cogenerator of the semigroup $(\tilde\tau_t)_{t\ge 0}$, {\it any singular} spectral type may be achieved by \gS_1 perturbations. We provide an explicit construction for a perturbation with a given spectral type based on the theory of model spaces of the Hardy space $H^2$. Also we show that we may obtain {\it any} prescribed spectral type for the unitary component of the perturbed semigroup by a perturbation from the class \gS_p with $p>1$