Energy, decay rate, and effective masses for a moving polaron in a Fermi sea: Explicit results in the weakly attractive limit

We study the properties of an impurity of mass $M$ moving through a spatially homogeneous three-dimensional fully polarized Fermi gas of particles of mass $m$. In the weakly attractive limit, where the effective coupling constant $g\to0^-$ and perturbation theory can be used, both for a broad and a narrow Feshbach resonance, we obtain an explicit analytical expression for the complex energy \Delta E(\KK) of the moving impurity up to order two included in $g$. This also gives access to its longitudinal and transverse effective masses m_\parallel^*(\KK), m_\perp^*(\KK), as functions of the impurity wave vector \KK. Depending on the modulus of \KK and on the impurity-to-fermion mass ratio $M/m$ we identify four regions separated by singularities in derivatives with respect to \KK of the second-order term of \Delta E(\KK), and we discuss the physical origin of these regions. Remarkably, the second-order term of m_\parallel^*(\KK) presents points of non-differentiability, replaced by a logarithmic divergence for $M=m$, when \KK is on the Fermi surface of the fermions. We also discuss the third-order contribution and relevance for cold atom experiments.Comment: 6 pages, 4 figures; final version, including a finite temperature calculatio

An impurity in a Fermi sea on a narrow Feshbach resonance: A variational study of the polaronic and dimeronic branches

We study the problem of a single impurity of mass $M$ immersed in a Fermi sea of particles of mass $m$. The impurity and the fermions interact through a s-wave narrow Feshbach resonance, so that the Feshbach length $R_*$ naturally appears in the system. We use simple variational ansatz, limited to at most one pair of particle-hole excitations of the Fermi sea and we determine for the polaronic and dimeronic branches the phase diagram between absolute ground state, local minimum, thermodynamically unstable regions (with negative effective mass), and regions of complex energies (with negative imaginary part). We also determine the closed channel population which is experimentally accessible. Finally we identify a non-trivial weakly attractive limit where analytical results can be obtained, in particular for the crossing point between the polaronic and dimeronic energy branches.Comment: 24 pages, 12 figure

Make It Simple and Light: Some Thoughts on Real Estate Related Taxation in China

This article discusses the advantages and disadvantages of real estate-related taxes that might be imposed in mainland China, in light of the government’s needs for tax revenue and the economy’s need for incentives to develop land. Some policy recommendations are presented, based on an analysis of real estate taxation in general and of China’s specific needs. As one recent article has noted, understanding how behavior adjusts in response to taxation is one of the most important issues in public finance.1China, Public Finance, Real Estate Taxation

Nonlinear Effects in Easement Valuation

Rules of thumb have been developed to assist appraisers in dealing with the uncertainties that abound when easement values must be estimated. An economic analysis of one popular rule-of-thumb technique, based on a fixed percentage of the value of a hypothetical fee simple interest in the affected land, reveals that such methodology could not generally be expected to yield meaningful results. If a rule of thumb were to be employed, its use would be more supportable if the underlying assumptions reflected the nonlinear structure of land values.

A projection operator approach to the Bose-Hubbard model

We develop a projection operator formalism for studying both the zero temperature equilibrium phase diagram and the non-equilibrium dynamics of the Bose-Hubbard model. Our work, which constitutes an extension of Phys. Rev. Lett. {\bf 106}, 095702 (2011), shows that the method provides an accurate description of the equilibrium zero temperature phase diagram of the Bose-Hubbard model for several lattices in two- and three-dimensions (2D and 3D). We show that the accuracy of this method increases with the coordination number $z_0$ of the lattice and reaches to within 0.5% of quantum Monte Carlo data for lattices with $z_0=6$. We compute the excitation spectra of the bosons using this method in the Mott and the superfluid phases and compare our results with mean-field theory. We also show that the same method may be used to analyze the non-equilibrium dynamics of the model both in the Mott phase and near the superfluid-insulator quantum critical point where the hopping amplitude $J$ and the on-site interaction $U$ satisfy $z_0J/U \ll 1$. In particular, we study the non-equilibrium dynamics of the model both subsequent to a sudden quench of the hopping amplitude $J$ and during a ramp from $J_i$ to $J_f$ characterized by a ramp time $\tau$ and exponent $\alpha$: $J(t)=J_i +(J_f-J_i) (t/\tau)^{\alpha}$. We compute the wavefunction overlap $F$, the residual energy $Q$, the superfluid order parameter $\Delta(t)$, the equal-time order parameter correlation function $C(t)$, and the defect formation probability $P$ for the above-mentioned protocols and provide a comparison of our results to their mean-field counterparts. We find that $Q$, $F$, and $P$ do not exhibit the expected universal scaling. We explain this absence of universality and show that our results for linear ramps compare well with the recent experimental observations.Comment: v2; new references and new sections adde

A Microeconomic Study of Commercial Real Estate Brokerage Firms

While residential brokerage has been widely studied, the operating characteristics on income property brokerage firms have received little attention in the literature. In this paper, we analyze results from a survey of income property brokers to measure profitability scale effects, and expenditures at the firm level. We find that while scale economies exist for expenses, net income per producer falls as firms grow; the optimally sized firm is comparatively small. Although inconsistencies with results from recent residential brokerage studies may relate to the survey period, they may also support a view that residential and income brokerage firms are structurally different.

Metastable states of a gas of dipolar bosons in a 2D optical lattice

We investigate the physics of dipolar bosons in a two dimensional optical lattice. It is known that due to the long-range character of dipole-dipole interaction, the ground state phase diagram of a gas of dipolar bosons in an optical lattice presents novel quantum phases, like checkerboard and supersolid phases. In this paper, we consider the properties of the system beyond its ground state, finding that it is characterised by a multitude of almost degenerate metastable states, often competing with the ground state. This makes dipolar bosons in a lattice similar to a disordered system and opens possibilities of using them for quantum memories.Comment: small improvements in the text, Fig.4 replaced, added and updated references. 4 pages, 4 figures, to appear in Phys. Rev. Let

Ultracold Dipolar Gases in Optical Lattices

This tutorial is a theoretical work, in which we study the physics of ultra-cold dipolar bosonic gases in optical lattices. Such gases consist of bosonic atoms or molecules that interact via dipolar forces, and that are cooled below the quantum degeneracy temperature, typically in the nK range. When such a degenerate quantum gas is loaded into an optical lattice produced by standing waves of laser light, new kinds of physical phenomena occur. These systems realize then extended Hubbard-type models, and can be brought to a strongly correlated regime. The physical properties of such gases, dominated by the long-range, anisotropic dipole-dipole interactions, are discussed using the mean-field approximations, and exact Quantum Monte Carlo techniques (the Worm algorithm).Comment: 56 pages, 26 figure

Non-equilibrium dynamics of the Bose-Hubbard model: A projection operator approach

We study the phase diagram and non-equilibrium dynamics, both subsequent to a sudden quench of the hopping amplitude $J$ and during a ramp $J(t)=Jt/\tau$ with ramp time $\tau$, of the Bose-Hubbard model at zero temperature using a projection operator formalism which allows us to incorporate the effects of quantum fluctuations beyond mean-field approximations in the strong coupling regime. Our formalism yields a phase diagram which provides a near exact match with quantum Monte Carlo results in three dimensions. We also compute the residual energy $Q$, the superfluid order parameter $\Delta(t)$, the equal-time order parameter correlation function $C(t)$, and the wavefunction overlap $F$ which yields the defect formation probability $P$ during non-equilibrium dynamics of the model. We find that $Q$, $F$, and $P$ do not exhibit the expected universal scaling. We explain this absence of universality and show that our results compare well with recent experiments.Comment: Replaced with the accepted version, added one figure. 4 pages, 4 figures, to appear in Phys. Rev. Let