Finite-Energy Spectral-Weight Distributions of a 1D Correlated Metal

We derive general closed-form analytical expressions for the finite-energy one- and two-electron spectral-weight distributions of an one-dimensional correlated metal with on-site electronic repulsion. Our results also provide general expressions for the one- and two-atom spectral functions of a correlated quantum system of cold fermionic atoms in a one-dimensional optical lattice with on-site atomic repulsion. In the limit of zero spin density our spectral-function expressions provide the correct zero-spin density results. Our results reveal the dominant non-perturbative microscopic many-particle mechanisms behind the exotic spectral properties observed in quasi-one-dimensional metals and correlated systems of cold fermionic atoms in one-dimensional optical lattices.Comment: 30 pages, no figure

The square-lattice quantum liquid of charge c fermions and spin-neutral two-spinon s1 fermions

The momentum bands, energy dispersions, and velocities of the charge $c$ fermions and spin-neutral two-spinon $s1$ fermions of a square-lattice quantum liquid referring to the Hubbard model on such a lattice of edge length $L$ in the one- and two-electron subspace are studied. The model involves the effective nearest-neighbor integral $t$ and on-site repulsion $U$ and can be experimentally realized in systems of correlated ultra-cold fermionic atoms on an optical lattice and thus our results are of interest for such systems. Our investigations profit from a general rotated-electron description, which is consistent with the model global $SO(3)\times SO(3)\times U(1)$ symmetry. For the model in the one- and two-electron subspace the discrete momentum values of the $c$ and $s1$ fermions are good quantum numbers so that in contrast to the original strongly-correlated electronic problem their interactions are residual. The use of our description renders an involved many-electron problem into a quantum liquid with some similarities with a Fermi liquid.Comment: 61 pages, 1 figure, published in Nuclear Physics

Exploring Periodic Orbit Expansions and Renormalisation with the Quantum Triangular Billiard

A study of the quantum triangular billiard requires consideration of a boundary value problem for the Green's function of the Laplacian on a trianglar domain. Our main result is a reformulation of this problem in terms of coupled non--singular integral equations. A non--singular formulation, via Fredholm's theory, guarantees uniqueness and provides a mathematically firm foundation for both numerical and analytic studies. We compare and contrast our reformulation, based on the exact solution for the wedge, with the standard singular integral equations using numerical discretisation techniques. We consider in detail the (integrable) equilateral triangle and the Pythagorean 3-4-5 triangle. Our non--singular formulation produces results which are well behaved mathematically. In contrast, while resolving the eigenvalues very well, the standard approach displays various behaviours demonstrating the need for some sort of ``renormalisation''. The non-singular formulation provides a mathematically firm basis for the generation and analysis of periodic orbit expansions. We discuss their convergence paying particular emphasis to the computational effort required in comparision with Einstein--Brillouin--Keller quantisation and the standard discretisation, which is analogous to the method of Bogomolny. We also discuss the generalisation of our technique to smooth, chaotic billiards.Comment: 50 pages LaTeX2e. Uses graphicx, amsmath, amsfonts, psfrag and subfigure. 17 figures. To appear Annals of Physics, southern sprin

Understanding economical outcomes with the mental number line

With this study we provide evidence that the cognitive processes involved in addition/subtraction, mapped along the mental number line, seem to mediate our understanding of trading verbs. When left-to-right culture participants read "loss" verbs, cognitive activation moves "leftward" as in arithmetical subtraction, while reading "gain" verbs activates a mental rightward space as in addition. 
 We test this hypothesis by asking to a group of participants to use their left and right hand in judging (as correct of not) the syntactic form of several verbs meaning financial outcomes. Results show that processing “gain verbs” was associated with shorter latencies when responding with the right hand similarly when performing an addition task, while processing “loss verbs” was associated with shorter latencies when responding with the left, similarly when performing a subtraction task. This finding suggests that understanding language denoting economics outcomes covertly engages the arithmetical system in a spatially left-right dimension. 
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Magnetic-field and chemical-potential effects on the low-energy separation

We show that in the presence of a magnetic field the usual low-energy separation of the Hubbard chain is replaced by a ``$c$'' and ``$s$'' separation. Here $c$ and $s$ refer to small-momentum and low-energy independent excitation modes which couple both to charge and spin. Importantly, we find the exact generators of these excitations both in the electronic and pseudoparticle basis. In the limit of zero magnetic field these generators become the usual charge and spin fluctuation operators. The $c$ and $s$ elementary excitations are associated with the $c$ and $s$ pseudoparticles, respectively. We also study the separate pseudoparticle left and right conservation laws. In the presence of the magnetic field the small-momentum and low-energy excitations can be bosonized. However, the suitable bosonization corresponds to the $c$ and $s$ pseudoparticle modes and not to the usual charge and spin fluctuations. We evaluate exactly the commutator between the electronic-density operators. Its spin-dependent factor is in general non diagonal and depends on the interaction. The associate bosonic commutation relations characterize the present unconventional low-energy separation.Comment: 29 pages, latex, submitted to Phys. Rev.

Charge and Spin Quantum Fluids Generated by Many-Electron Interactions

In this paper we describe the electrons of the 1D Hubbard model by a fluid of unpaired rotated electrons and a fluid of zero-spin rotated-electron pairs. The rotated electrons are related to the original electrons by a mere unitary transformation. For all finite values of energy and for the whole parameter space of the model this two-fluid picture leads to a description of the energy eigenstates in terms of occupancy configurations of $\eta$-spin 1/2 holons, spin 1/2 spinons, and $c$ pseudoparticles only. The electronic degrees of freedom couple to external charge (and spin) probes through the holons and $c$ pseudoparticles (and spinons). Our results refer to very large values of the number of lattice sites $N_a$. The holon (and spinon) charge (and spin transport is made by $2\nu$-holon (and $2\nu$-spinon) composite pseudoparticles such that $\nu=1,2,...$.Comment: 25 pages, no figure

Derived moduli of complexes and derived Grassmannians

In the first part of this paper we construct a model structure for the category of filtered cochain complexes of modules over some commutative ring $R$ and explain how the classical Rees construction relates this to the usual projective model structure over cochain complexes. The second part of the paper is devoted to the study of derived moduli of sheaves: we give a new proof of the representability of the derived stack of perfect complexes over a proper scheme and then use the new model structure for filtered complexes to tackle moduli of filtered derived modules. As an application, we construct derived versions of Grassmannians and flag varieties.Comment: 54 pages, Section 2.4 significantly extended, minor corrections to the rest of the pape

Strategy-proof coalition formation

We analyze coalition formation problems in which a group of agents is partitioned into coalitions and agents' preferences only depend on the coalition they belong to. We study rules that associate to each profile of agents' preferences a partition of the society. We focus on strategyproof rules on restricted domains of preferences, as the domains of additively representable or separable preferences. In such domains, only single-lapping rules satisfy strategy-proofness, individual rationality, non-bossiness, and flexibility. Single-lapping rules are characterized by severe restrictions on the set of feasible coalitions. These restrictions are consistent with hierarchical organizations and imply that single-lapping rules always select core-stable partitions. Thus, our results highlight the relation between the non-cooperative concept of strategy-proofness and the cooperative concept of core-stability. We analyze the implications of our results for matching problem

Selective bias in temporal bisection task by number exposition

Temporal experience can be modulated by a number of environmental factors such as quantity. Here I show that merely looking at numbers causes a bias in imaginative (but not perceptual) time bisection task that depends on the number’s magnitude. This suggests that automatic shifts of spatial attention to the left and right side, as a result of exposure to numbers, modulates temporal as well as spatial behaviour (2,3,4). This finding suggests that the representation of time and space produce certain patterns in neural maps that are decoded by means of the similar neural mechanisms