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"Theoretical mathematics”: Toward a cultural synthesis of mathematics and theoretical physics
 BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY
, 1993
"... Is speculative mathematics dangerous? Recent interactions between physics and mathematics pose the question with some force: traditional mathematical norms discourage speculation, but it is the fabric of theoretical physics. In practice there can be benefits, but there can also be unpleasant and de ..."
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Cited by 24 (1 self)
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Is speculative mathematics dangerous? Recent interactions between physics and mathematics pose the question with some force: traditional mathematical norms discourage speculation, but it is the fabric of theoretical physics. In practice there can be benefits, but there can also be unpleasant and destructive consequences. Serious caution is required, and the issue should be considered before, rather than after, obvious damage occurs. With the hazards carefully in mind, we propose a framework that should allow a healthy and positive role for speculation.
Frustrated quantum magnets
 Lecture Notes in Physics 595
, 2002
"... A description of different phases of two dimensional magnetic insulators is given. The first chapters are devoted to the understanding of the symmetry breaking mechanism in the semiclassical Néel phases. Order by disorder selection is illustrated. All these phases break SU(2) symmetry and are gaple ..."
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Cited by 2 (0 self)
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A description of different phases of two dimensional magnetic insulators is given. The first chapters are devoted to the understanding of the symmetry breaking mechanism in the semiclassical Néel phases. Order by disorder selection is illustrated. All these phases break SU(2) symmetry and are gapless phases with ∆Sz = 1 magnon excitations. Different gapful quantum phases exist in two dimensions: the Valence Bond Crystal phases (VBC) which have long range order in local S=0 objects (either dimers in the usual Valence Bond acception or quadrumers..), but also Resonating Valence Bond Spin Liquids (RVBSL), which have no long range order in any local order parameter and an absence of susceptibility to any local probe. VBC have gapful ∆S = 0, or1 excitations, RVBSL on the contrary have deconfined spin1/2 excitations. Examples of these two kinds of quantum phases are given in chapters 4 and 5. A special class of magnets (on the kagome or pyrochlore lattices) has an infinite local degeneracy in the classical limit: they give birth in the quantum limit to different behaviors which are illustrated and questionned in the last lecture.
THE TIGHTBINDING APPROACH TO THE DIELECTRIC RESPONSE IN THE MULTIBAND SYSTEMS
, 1995
"... Starting from the random phase approximation for the weakly coupled multiband tightlybounded electron systems, we calculate the dielectric matrix in terms of intraband and interband transitions. The advantages of this representation with respect to the usual planewave decomposition are pointed out ..."
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Starting from the random phase approximation for the weakly coupled multiband tightlybounded electron systems, we calculate the dielectric matrix in terms of intraband and interband transitions. The advantages of this representation with respect to the usual planewave decomposition are pointed out. The analysis becomes particularly transparent in the long wavelength limit, after performing the multipole expansion of bare Coulomb matrix elements. For illustration, the collective modes and the macroscopic dielectric function for a general cubic lattice are derived. It is shown that the dielectric instability in conducting narrow band systems proceeds by a common softening of one transverse and one longitudinal mode. Furthermore, the selfpolarization corrections which appear in the macroscopic dielectric function for finite band sys1 tems, are identified as a combined effect of intraatomic exchange interactions between electrons sitting in different orbitals and a finite interatomic tunneling. PACS: 71.10.+x, 71.45.Gm Key words: random phase approximation, dielectric matrix, collective modes, selfpolarization corrections 2 1
Dielectric properties of multiband electron systems: II Collective modes
, 1996
"... Starting from the tightbinding dielectric matrix in the random phase approximation we examine the collective modes and electronhole excitations in a twoband electronic system. For long wavelengths (q → 0), for which most of the analysis is carried out, the properties of the collective modes are c ..."
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Starting from the tightbinding dielectric matrix in the random phase approximation we examine the collective modes and electronhole excitations in a twoband electronic system. For long wavelengths (q → 0), for which most of the analysis is carried out, the properties of the collective modes are closely related to the symmetry of the atomic orbitals involved in the tightbinding states. In insulators there are only interband charge oscillations. If atomic dipolar transitions are allowed, the corresponding collective modes reduce in the asymptotic limit of vanishing bandwidths to Frenkel excitons for an atomic insulator with weak onsite interactions. The finite bandwidths renormalize the dispersion of these modes and introduce a continuum of incoherent interband electronhole excitations. The possible Landau damping of collective modes due to the presence of this continuum is discussed in detail. 1 In conductors the intraband charge fluctuations give rise to plasmons. If the atomic dipolar transitions are forbidden, the coupling of interband collective modes and plasmons tends to zero as q → 0. On the contrary, in dipolar conductors this coupling is strong and nonperturbative, due to the long range monopoledipole interaction between intraband and interband charge fluctuations. The resulting collective modes are hybrids of intraband plasmons and interband dipolar oscillations. It is shown that the frequency of the lower hybridized longitudinal mode is proportional to the frequency of the transverse dipolar mode when the latter is small. The dielectric instability in a multiband conductor is therefore characterized by the simultaneous softening of a transverse and a longitudinal mode, which is an important, directly measurable consequence of the present theory. PACS: 71.45.d Key words: collective modes, Landau damping, dielectric instability
unknown title
, 2001
"... www.elsevier.com/locate/pla Fokker–Planck analysis of the nonlinear field dependence of a carrier in a band at arbitrary temperatures P.E. Parris a,M.Ku´s b,V.M.Kenkre c,∗ ..."
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www.elsevier.com/locate/pla Fokker–Planck analysis of the nonlinear field dependence of a carrier in a band at arbitrary temperatures P.E. Parris a,M.Ku´s b,V.M.Kenkre c,∗