18062907
Damping of collective nuclear motion and thermodynamic properties of nuclei beyond mean field
Abstract The dynamical description of correlated nuclear motion is based on a set of coupled equations of motion for the one-body density matrix ϱ (11′; t ) and the two-body correlation function c 2 (12, 1′2′; t ), which is obtained from the density-matrix hierarchy beyond conventional mean-field approaches by truncating three-body correlations. The resulting equations non-perturbatively describe particle-particle collisions (short-range correlations) as well as particle-hole interactions (long-range correlations). Within a basis of time-dependent Hartree-Fock states these equations of motion are solved for collective vibrations of 40 Ca at several finite thermal excitation energies corresponding to temperatures T = 0 – 6 MeV. Transport coefficients for friction and diffusion are extracted from the explicit solutions in comparison to the solutions of the associated TDHF, VUU, Vlasov or damped quantum oscillator equations of motion. We find that the actual magnitude of the transport coefficients is strongly influenced by particle-hole correlations at low temperature which generate large fluctuations in the nuclear shape degrees of freedom. Thermodynamically, the specific heat and the entropy of the system as a function of temperature does not differ much from the mean-field limit except for a bump in the specific heat around T ⋍ MeV which we attribute to the melting of shell effects in the correlated system.
121072448
On the Nonautonomous Nonlinear Schrödinger Equations and Soliton Management
We present some novel results on the nonlinear Schrodinger equations with time‐ and space‐dependent dispersion, nonlinearity, dissipation/gain and external potentials which read i∂u(x,t)∂t+f(x,t)∂2u(x,t)∂x2+g(x,t)|u(x,t)|2u(x,t)+V(x,t)u(x,t)+iγ(x,t)u(x,t) = 0. Based on these results, we show some explicit ways to control the soliton dynamics in some physically interesting nonlinear systems like Bose‐Einstein condensates and optical soliton transmission.
118708688
Extended dual description of Mott transition beyond two-dimensional space
Motivated by recent work of Mross and Senthil [Phys. Rev. B \textbf{84}, 165126 (2011)] which provides a dual description for Mott transition from Fermi liquid to quantum spin liquid in two space dimensions, we extend their approach to higher dimensional cases, and we provide explicit formalism in three space dimensions. Instead of the vortices driving conventional Fermi liquid into quantum spin liquid states in 2D, it is the vortex lines to lead to the instability of Fermi liquid in 3D. The extended formalism can result in rich consequences when the vortex lines condense in different degrees of freedom. For example, when the vortex lines condense in charge phase degrees of freedom, the resulting effective fermionic action is found to be equivalent to that obtained by well-studied slave-particle approaches for Hubbard and/or Anderson lattice models, which confirm the validity of the extended dual formalism in 3D. When the vortex lines condense in spin phase degrees of freedom, a doublon metal with a spin gap and an instability to the unconventional superconducting pairing can be obtained. In addition, when the vortex lines condense in both phase degrees, an exotic doubled U(1) gauge theory occurs which describes a separation of spin-opposite fermionic excitations. It is noted that the first two features have been discussed in a similar way in 2D, the last one has not been reported in the previous works. The present work is expected to be useful in understanding the Mott transition happening beyond two space dimensions.
119114164
A note on path integral formulism of Z2 slave-spin representation of Hubbard model
(4)where a ferromagnetic coupling J > 0 is assumed and Krepresents the the transverse external ﬁeld.At ﬁrst sight, one may directly use the coherent stateof spin operator in constructing the path integral rep-resentation, (One can ﬁnd a brief but useful introduc-tion to this issue in Ref. 9.) however, this will lead toan extra topological Berry phase term and is not easyto utilize practically. An alterative approach is to usethe eigenstates of spin operator τ
118605638
Subleading soft behavior of QCD amplitudes
We elaborate on the radiative behaviour of tree-level scattering amplitudes in the soft regime. We show that the sub-leading soft term in single-gluon emission of quark-gluon amplitudes in QCD is controlled by differential operators, whose universal form can be derived from both on-shell recursion relation and gauge invariance, as it was shown to hold for graviton- and gluon-scattering.