The Use of Real Estate for the Settlement of Claims in Roman Palestine

The Mishna in Tractate Gittin discusses land qualities, in a context where land is used to settle monetary obligations. The law is that land of different qualities must be used to pay claimants in different situations; in particular, claimants pursuant to a tort case have the right to have their claim paid with land of the best quality. Creditors have the right to be paid with land of medium quality, while women who are owed money as part of a ketuba (marriage contract) claim may have to be satisfied with land of the lowest quality. However, the total value of the land received by each claimant is just the amount they are owed it is independent of the quality of the land that is used to pay them. This being the case, the purpose of the legislation is unclear. In this paper, I explore the possibility that the law is designed to minimize the total amount of transactions costs.Land markets, Law, religion and economics, Market microstructure, mishna, sasanian babylonia, Talmud

Stable manifolds and homoclinic points near resonances in the restricted three-body problem

The restricted three-body problem describes the motion of a massless particle under the influence of two primaries of masses $1-\mu$ and $\mu$ that circle each other with period equal to $2\pi$. For small $\mu$, a resonant periodic motion of the massless particle in the rotating frame can be described by relatively prime integers $p$ and $q$, if its period around the heavier primary is approximately $2\pi p/q$, and by its approximate eccentricity $e$. We give a method for the formal development of the stable and unstable manifolds associated with these resonant motions. We prove the validity of this formal development and the existence of homoclinic points in the resonant region. In the study of the Kirkwood gaps in the asteroid belt, the separatrices of the averaged equations of the restricted three-body problem are commonly used to derive analytical approximations to the boundaries of the resonances. We use the unaveraged equations to find values of asteroid eccentricity below which these approximations will not hold for the Kirkwood gaps with $q/p$ equal to 2/1, 7/3, 5/2, 3/1, and 4/1. Another application is to the existence of asymmetric librations in the exterior resonances. We give values of asteroid eccentricity below which asymmetric librations will not exist for the 1/7, 1/6, 1/5, 1/4, 1/3, and 1/2 resonances for any $\mu$ however small. But if the eccentricity exceeds these thresholds, asymmetric librations will exist for $\mu$ small enough in the unaveraged restricted three-body problem

Dimer and N\'eel order-parameter fluctuations in the spin-fluid phase of the s=1/2 spin chain with first and second neighbor couplings

The dynamical properties at T=0 of the one-dimensional (1D) s=1/2 nearest-neighbor (nn) XXZ model with an additional isotropic next-nearest-neighbor (nnn) coupling are investigated by means of the recursion method in combination with techniques of continued-fraction analysis. The focus is on the dynamic structure factors S_{zz}(q,\omega) and S_{DD}(q,\omega), which describe (for q=\pi) the fluctuations of the N\'eel and dimer order parameters, respectively. We calculate (via weak-coupling continued-fraction analysis) the dependence on the exchange constants of the infrared exponent, the renormalized bandwidth of spinon excitations, and the spectral-weight distribution in S_{zz}(\pi,\omega) and S_{DD}(\pi,\omega), all in the spin-fluid phase, which is realized for planar $nn$ anisotropy and sufficiently weak nnn coupling. For some parameter values we find a discrete branch of excitations above the spinon continuum. They contribute to S_{zz}(q,\omega) but not to S_{DD}(q,\omega).Comment: RevTex file (7 pages), 8 figures (uuencoded ps file) available from author

Systematic Mapping of the Hubbard Model to the Generalized t-J Model

The generalized t-J model conserving the number of double occupancies is constructed from the Hubbard model at and in the vicinity of half-filling at strong coupling. The construction is realized by a self-similar continuous unitary transformation. The flow equation is closed by a truncation scheme based on the spatial range of processes. We analyze the conditions under which the t-J model can be set up and we find that it can only be defined for sufficiently large interaction. There, the parameters of the effective model are determined.Comment: 16 pages, 13 figures included. v2: Order of sections changed. Calculation and discussion of apparent gap in Section IV.A correcte

COMPLETE SOLUTION OF THE XXZ-MODEL ON FINITE RINGS. DYNAMICAL STRUCTURE FACTORS AT ZERO TEMPERATURE.

The finite size effects of the dynamical structure factors in the XXZ-model are studied in the euclidean time $(\tau)$-representation. Away from the critical momentum $p=\pi$ finite size effects turn out to be small except for the large $\tau$ limit. The large finite size effects at the critical momentum $p=\pi$ signal the emergence of infrared singularities in the spectral $(\omega)$-representation of the dynamical structure factors.Comment: PostScript file with 12 pages + 11 figures uuencoded compresse

Dynamics of spin correlations in the spin-1/2 isotropic XY chain in a transverse field

Dynamic xx spin pair correlation functions for the isotropic spin-1/2 XY chain are calculated numerically for long open chains in the presence of a transverse magnetic field at finite temperature. As an application we discuss the temperature dependence of the spin-spin relaxation time in PrCl_3.Comment: 2 pages, latex, 2 figures, abstract of the paper presented at Ampere Summer School ``Applications of Magnetic Resonance in Novel Materials'' Nafplion, Greece, 3-9 September, 2000, partially published in J. Phys. A: Math. Gen. 33, 3063 (2000

Adapted continuous unitary transformation to treat systems with quasiparticles of finite lifetime

An improved generator for continuous unitary transformations is introduced to describe systems with unstable quasiparticles. Its general properties are derived and discussed. To illustrate this approach we investigate the asymmetric antiferromagnetic spin-1/2 Heisenberg ladder which allows for spontaneous triplon decay. We present results for the low energy spectrum and the momentum resolved spectral density of this system. In particular, we show the resonance behavior of the decaying triplon explicitly.Comment: 40 pages, 12 figure

Thermal and ground-state entanglement in Heisenberg XX qubit rings

We study the entanglement of thermal and ground states in Heisernberg $XX$ qubit rings with a magnetic field. A general result is found that for even-number rings pairwise entanglement between nearest-neighbor qubits is independent on both the sign of exchange interaction constants and the sign of magnetic fields. As an example we study the entanglement in the four-qubit model and find that the ground state of this model without magnetic fields is shown to be a four-body maximally entangled state measured by the $N$-tangle.Comment: Four pages and one figure, small change

Continuous slice functional calculus in quaternionic Hilbert spaces

The aim of this work is to define a continuous functional calculus in quaternionic Hilbert spaces, starting from basic issues regarding the notion of spherical spectrum of a normal operator. As properties of the spherical spectrum suggest, the class of continuous functions to consider in this setting is the one of slice quaternionic functions. Slice functions generalize the concept of slice regular function, which comprises power series with quaternionic coefficients on one side and that can be seen as an effective generalization to quaternions of holomorphic functions of one complex variable. The notion of slice function allows to introduce suitable classes of real, complex and quaternionic $C^*$--algebras and to define, on each of these $C^*$--algebras, a functional calculus for quaternionic normal operators. In particular, we establish several versions of the spectral map theorem. Some of the results are proved also for unbounded operators. However, the mentioned continuous functional calculi are defined only for bounded normal operators. Some comments on the physical significance of our work are included.Comment: 71 pages, some references added. Accepted for publication in Reviews in Mathematical Physic