We study the magnetoelectric coupling at the surface of a topological insulator. We are particularly interested in the surface current induced by a static Zeeman/exchange field. This surface current can be related to the orbital magnetization of the system. For an insulator with zero Chern number, the orbital magnetization is independent of the details at the boundary. With the appearance of su...

The rotational specific heat of molecular hydrogen in the old quantum theory Max Planck Institute for the History of Science, Berlin, 13–16 June 2006 Clayton Gearhart (St. John’s University, Minnesota, USA) “Astonishing successes” and “bitter disappointment”: Thus did the German physicist Fritz Reiche portray the state of quantum theory in his 1921 text. His words apply in miniature to early de...

We construct the path integral for one-dimensional non-linear sigma models, starting from a given Hamiltonian operator and states in a Hilbert space. By explicit evaluation of the discretized propagators and vertices we find the correct Feynman rules which differ from those often assumed. These rules, which we previously derived in bosonic systems [1], are now extended to fermionic systems. We ...

Due to the Heisenberg uncertainty principle, various classical systems differing only on the scale smaller than Planck's cell correspond to the same quantum system. We use this fact to find a unique semiclassical representation without the Van Vleck determinant, applicable to a large class of correlation functions expressible as quantum fidelity. As in the Feynman path integral formulation of q...

Anharmonic vibrational states of semirigid polyatomic molecules are often studied using the second-order vibrational perturbation theory (VPT2). For efficient higher-order analysis, an approach based on the canonical Van Vleck perturbation theory (CVPT), the Watson Hamiltonian and operators of creation and annihilation of vibrational quanta is employed. This method allows analysis of the conver...

We develop a theory describing the effects of many–particle Coulomb correlations on the coherent ultrafast nonlinear optical response of semiconductors and metals. Our approach is based on a mapping of the nonlinear optical response of the “bare” system onto the linear response of a “dressed” system. The latter is characterized by effective time–dependent optical transition matrix elements, ele...

The semiclassical approximation for a quantum amplitude is given by the sum of contributions from intersections of the appropriate manifolds in classical phase space. The intersection overlaps are just the Van Vleck determinants multiplied by a phase given by a classical action. Here we consider two nonstandard instances of this semiclassical prescription which would appear to be on shaky groun...

The magnetization, specific heat and electrical resistivity of PrRhIn5 compound were studied. High quality crystals of PrRhIn5 and LaRhIn5, which adopt the tetragonal HoCoGa5-type (P4/mmm) structure, were prepared by solution growth. In the range 150 320 K the susceptibility χ follows the Curie-Weiss law. For PrRhIn5 the effective moment μeff and paramagnetic Curie temperature θp are μeff = 3. ...

Abstract. In this paper we review some applications of the path integral methodology of quantum mechanics to financial modeling and options pricing. A path integral is defined as a limit of the sequence of finite-dimensional integrals, in a much the same way as the Riemannian integral is defined as a limit of the sequence of finite sums. The risk-neutral valuation formula for path-dependent opt...

All seven physics STAIRSTEP students and 15 undergraduate students have participated to a talk about the orbital magnetic susceptibility of electrons in a rectangular box. Mesoscopic systems, such as small metal particles and quantum dots, exhibit many novel properties due to the coherent effect and finite-size quantization. In the mesoscopic regime, magnetic properties are sensitive to whether...