Scattering by a contact potential in three and lower dimensions

We consider the scattering of nonrelativistic particles in three dimensions by a contact potential $\Omega\hbar^2\delta(r)/ 2\mu r^\alpha$ which is defined as the $a\to 0$ limit of $\Omega\hbar^2\delta(r-a)/2\mu r^\alpha$. It is surprising that it gives a nonvanishing cross section when $\alpha=1$ and $\Omega=-1$. When the contact potential is approached by a spherical square well potential instead of the above spherical shell one, one obtains basically the same result except that the parameter $\Omega$ that gives a nonvanishing cross section is different. Similar problems in two and one dimensions are studied and results of the same nature are obtained.Comment: REVTeX, 9 pages, no figur

Electron-positron pair creation in a vacuum by an electromagnetic field in 3+1 and lower dimensions

We calculate the probability of electron-positron pair creation in vacuum in 3+1 dimensions by an external electromagnetic field composed of a constant uniform electric field and a constant uniform magnetic field, both of arbitrary magnitudes and directions. The same problem is also studied in 2+1 and 1+1 dimensions in appropriate external fields and similar results are obtained.Comment: REVTeX, 10 pages, no figure, a brief note and some more references added in the proo

Interviewing During a Tight Job Market

Various tips for interviewing for PhD graduates, seeking an academic position in a research university in Asia or North America are discussed. It is suggested that having the dissertation done before interviews gives a large degree of relief on one\u27s mind. It is found that to be practical about job research package and keep a close eye on applications increases the confidence level. It is also observed that the questions during the talk provides opportunity to clarify and strengthen the talk and show this ability during the interview

Charged particles in a rotating magnetic field

We study the valence electron of an alkaline atom or a general charged particle with arbitrary spin and with magnetic moment moving in a rotating magnetic field. By using a time-dependent unitary transformation, the Schr\"odinger equation with the time-dependent Hamiltonian can be reduced to a Schr\"odinger-like equation with a time-independent effective Hamiltonian. Eigenstates of the effective Hamiltonian correspond to cyclic solutions of the original Schr\"odinger equation. The nonadiabatic geometric phase of a cyclic solution can be expressed in terms of the expectation value of the component of the total angular momentum along the rotating axis, regardless of whether the solution is explicitly available. For the alkaline atomic electron and a strong magnetic field, the eigenvalue problem of the effective Hamiltonian is completely solved, and the geometric phase turns out to be a linear combination of two solid angles. For a weak magnetic field, the same problem is solved partly. For a general charged particle, the problem is solved approximately in a slowly rotating magnetic field, and the geometric phases are also calculated.Comment: REVTeX, 13 pages, no figure. There are two minor errors in the published version due to incorrect editing by the publisher. The "spin-1" in Sec. I and the "spin 1" in Sec. II below Eq. (2c) should both be changed to "spin" or "spin angular momentum". The preferred E-mail for correspondence is [email protected] or [email protected]

Geometric phases for neutral and charged particles in a time-dependent magnetic field

It is well known that any cyclic solution of a spin 1/2 neutral particle moving in an arbitrary magnetic field has a nonadiabatic geometric phase proportional to the solid angle subtended by the trace of the spin. For neutral particles with higher spin, this is true for cyclic solutions with special initial conditions. For more general cyclic solutions, however, this does not hold. As an example, we consider the most general solutions of such particles moving in a rotating magnetic field. If the parameters of the system are appropriately chosen, all solutions are cyclic. The nonadiabatic geometric phase and the solid angle are both calculated explicitly. It turns out that the nonadiabatic geometric phase contains an extra term in addition to the one proportional to the solid angle. The extra term vanishes automatically for spin 1/2. For higher spin, however, it depends on the initial condition. We also consider the valence electron of an alkaline atom. For cyclic solutions with special initial conditions in an arbitrary strong magnetic field, we prove that the nonadiabatic geometric phase is a linear combination of the two solid angles subtended by the traces of the orbit and spin angular momenta. For more general cyclic solutions in a strong rotating magnetic field, the nonadiabatic geometric phase also contains extra terms in addition to the linear combination.Comment: revtex, 18 pages, no figur

Vacuum polarization for neutral particles in 2+1 dimensions

In 2+1 dimensions there exists a duality between a charged Dirac particle coupled minimally to a background vector potential and a neutral one coupled nonminimally to a background electromagnetic field strength. A constant uniform background electric current induces in the vacuum of the neutral particle a fermion current which is proportional to the background one. A background electromagnetic plane wave induces no current in the vacuum. For constant but nonuniform background electric charge, known results for charged particles can be translated to give the induced fermion number. Some new examples with infinite background electric charge are presented. The induced spin and total angular momentum are also discussed.Comment: REVTeX, 7 pages, no figur

Topology and geometry under the nonlinear electromagnetic spotlight

For many materials, a precise knowledge of their dispersion spectra is insufficient to predict their ordered phases and physical responses. Instead, these materials are classified by the geometrical and topological properties of their wavefunctions. A key challenge is to identify and implement experiments that probe or control these quantum properties. In this review, we describe recent progress in this direction, focusing on nonlinear electromagnetic responses that arise directly from quantum geometry and topology. We give an overview of the field by discussing new theoretical ideas, groundbreaking experiments, and the novel materials that drive them. We conclude by discussing how these techniques can be combined with new device architectures to uncover, probe, and ultimately control novel quantum phases with emergent topological and correlated properties.Comment: Nature Materials (In Press

Perdeuterated cyanobiphenyl liquid crystals for infrared applications

Perdeuterated 4'-pentyl-4-cyanobiphenyl (D5CB) was synthesized and its physical properties evaluated and compared to those of 5CB. D5CB retains physical properties similar to those of 5CB, such as phase transition temperatures, dielectric constants, and refractive indices. An outstanding feature of D5CB is that it exhibits a much cleaner and reduced infrared absorption. Perdeuteration, therefore, extends the usable range of liquid crystals to the mid infrared by significantly reducing the absorption in the near infrared, which is essential for telecom applications

Half-metallic ferromagnetism and structural stability of zincblende phases of the transition-metal chalcogenides

An accurate density-functional method is used to study systematically half-metallic ferromagnetism and stability of zincblende phases of 3d-transition-metal chalcogenides. The zincblende CrTe, CrSe, and VTe phases are found to be excellent half-metallic ferromagnets with large half-metallic gaps (up to 0.88 eV). They are mechanically stable and approximately 0.31-0.53 eV per formula unit higher in total energy than the corresponding nickel-arsenide ground-state phases, and therefore would be grown epitaxially in the form of films and layers thick enough for spintronic applications.Comment: 4 pages with 4 figures include