18,636 research outputs found

### Market Equilibrium with Transaction Costs

Identical products being sold at different prices in different locations is a
common phenomenon. Price differences might occur due to various reasons such as
shipping costs, trade restrictions and price discrimination. To model such
scenarios, we supplement the classical Fisher model of a market by introducing
{\em transaction costs}. For every buyer $i$ and every good $j$, there is a
transaction cost of \cij; if the price of good $j$ is $p_j$, then the cost to
the buyer $i$ {\em per unit} of $j$ is p_j + \cij. This allows the same good
to be sold at different (effective) prices to different buyers.
We provide a combinatorial algorithm that computes $\epsilon$-approximate
equilibrium prices and allocations in
$O\left(\frac{1}{\epsilon}(n+\log{m})mn\log(B/\epsilon)\right)$ operations -
where $m$ is the number goods, $n$ is the number of buyers and $B$ is the sum
of the budgets of all the buyers

### Geometric-Phase-Effect Tunnel-Splitting Oscillations in Single-Molecule Magnets with Fourth-Order Anisotropy Induced by Orthorhombic Distortion

We analyze the interference between tunneling paths that occurs for a spin
system with both fourth-order and second-order transverse anisotropy. Using an
instanton approach, we find that as the strength of the second-order transverse
anisotropy is increased, the tunnel splitting is modulated, with zeros
occurring periodically. This effect results from the interference of four
tunneling paths connecting easy-axis spin orientations and occurs in the
absence of any magnetic field.Comment: 6 pages, 5 eps figures. Version published in EPL. Expanded from v1:
Appendix added, references added, 1 figure added, others modified
cosmeticall

### On the extra phase correction to the semiclassical spin coherent-state propagator

The problem of an origin of the Solary-Kochetov extra-phase contribution to
the naive semiclassical form of a generalized phase-space propagator is
addressed with the special reference to the su(2) spin case which is the most
important in applications. While the extra-phase correction to a flat
phase-space propagator can straightforwardly be shown to appear as a difference
between the principal and the Weyl symbols of a Hamiltonian in the
next-to-leading order expansion in the semiclassical parameter, the same
statement for the semiclassical spin coherent-state propagator holds provided
the Holstein-Primakoff representation of the su(2) algebra generators is
employed.Comment: 19 pages, no figures; a more general treatment is presented, some
references are added, title is slightly changed; submitted to JM

### Are Panel Unit Root Tests Useful for Real-Time Data?

With the development of real-time databases, N vintages are available for T observations instead of a single realization of the time series process. Although the use of panel unit root tests with the aim to gain in efficiency seems obvious, empirical and simulation results shown in this paper heavily mitigate the intuitive perspective.macroeconomics ;

### Quantitative weighted estimates for Rubio de Francia's Littlewood--Paley square function

We consider the Rubio de Francia's Littlewood--Paley square function
associated with an arbitrary family of intervals in $\mathbb{R}$ with finite
overlapping. Quantitative weighted estimates are obtained for this operator.
The linear dependence on the characteristic of the weight $[w]_{A_{p/2}}$ turns
out to be sharp for $3\le p<\infty$, whereas the sharpness in the range $2<p<3$
remains as an open question. Weighted weak-type estimates in the endpoint $p=2$
are also provided. The results arise as a consequence of a sparse domination
shown for these operators, obtained by suitably adapting the ideas coming from
Benea (2015) and Culiuc et al. (2016).Comment: 18 pages. Revised versio

### Oscillatory Tunnel Splittings in Spin Systems: A Discrete Wentzel-Kramers-Brillouin Approach

Certain spin Hamiltonians that give rise to tunnel splittings that are viewed
in terms of interfering instanton trajectories, are restudied using a discrete
WKB method, that is more elementary, and also yields wavefunctions and
preexponential factors for the splittings. A novel turning point inside the
classically forbidden region is analysed, and a general formula is obtained for
the splittings. The result is appled to the \Fe8 system. A previous result for
the oscillation of the ground state splitting with external magnetic field is
extended to higher levels.Comment: RevTex, one ps figur

### Fragility of the Commons under Prospect-Theoretic Risk Attitudes

We study a common-pool resource game where the resource experiences failure
with a probability that grows with the aggregate investment in the resource. To
capture decision making under such uncertainty, we model each player's risk
preference according to the value function from prospect theory. We show the
existence and uniqueness of a pure Nash equilibrium when the players have
heterogeneous risk preferences and under certain assumptions on the rate of
return and failure probability of the resource. Greater competition, vis-a-vis
the number of players, increases the failure probability at the Nash
equilibrium; we quantify this effect by obtaining bounds on the ratio of the
failure probability at the Nash equilibrium to the failure probability under
investment by a single user. We further show that heterogeneity in attitudes
towards loss aversion leads to higher failure probability of the resource at
the equilibrium.Comment: Accepted for publication in Games and Economic Behavior, 201

### Doping a correlated band insulator: A new route to half metallic behaviour

We demonstrate in a simple model the surprising result that turning on an
on-site Coulomb interaction U in a doped band insulator leads to the formation
of a half-metallic state. In the undoped system, we show that increasing U
leads to a first order transition between a paramagnetic, band insulator and an
antiferomagnetic Mott insulator at a finite value U_{AF}. Upon doping, the
system exhibits half metallic ferrimagnetism over a wide range of doping and
interaction strengths on either side of U_{AF}. Our results, based on dynamical
mean field theory, suggest a novel route to half-metallic behavior and provide
motivation for experiments on new materials for spintronics.Comment: 5 pages, 7 figure

### Phase Diagram of the Half-Filled Ionic Hubbard Model

We study the phase diagram of the ionic Hubbard model (IHM) at half-filling
using dynamical mean field theory (DMFT), with two impurity solvers, namely,
iterated perturbation theory (IPT) and continuous time quantum Monte Carlo
(CTQMC). The physics of the IHM is governed by the competition between the
staggered potential $\Delta$ and the on-site Hubbard U. In both the methods we
find that for a finite $\Delta$ and at zero temperature, anti-ferromagnetic
(AFM) order sets in beyond a threshold $U=U_{AF}$ via a first order phase
transition below which the system is a paramagnetic band insulator. Both the
methods show a clear evidence for a transition to a half-metal phase just after
the AFM order is turned on, followed by the formation of an AFM insulator on
further increasing U. We show that the results obtained within both the methods
have good qualitative and quantitative consistency in the intermediate to
strong coupling regime. On increasing the temperature, the AFM order is lost
via a first order phase transition at a transition temperature $T_{AF}(U,
\Delta)$ within both the methods, for weak to intermediate values of U/t. But
in the strongly correlated regime, where the effective low energy Hamiltonian
is the Heisenberg model, IPT is unable to capture the thermal (Neel) transition
from the AFM phase to the paramagnetic phase, but the CTQMC does. As a result,
at any finite temperature T, DMFT+CTQMC shows a second phase transition (not
seen within DMFT+IPT) on increasing U beyond $U_{AF}$. At $U_N > U_{AF}$, when
the Neel temperature $T_N$ for the effective Heisenberg model becomes lower
than T, the AFM order is lost via a second order transition. In the
3-dimensonal parameter space of $(U/t,T/t,\Delta/t)$, there is a line of
tricritical points that separates the surfaces of first and second order phase
transitions.Comment: Revised versio

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