On the spectrum of the periodic Dirac operator

The absolute continuity of the spectrum for the periodic Dirac operator $$\hat D=\sum_{j=1}^n(-i\frac {\partial}{\partial x_j}-A_j)\hat \alpha_j + \hat V^{(0)}+\hat V^{(1)}, x\in R^n, n\geq 3,$$ is proved given that either $A\in C(R^n;R^n)\cap H^q_{loc}(R^n;R^n)$, 2q > n-2, or the Fourier series of the vector potential $A:R^n\to R^n$ is absolutely convergent. Here, $\hat V^{(s)}=(\hat V^{(s)})^*$ are continuous matrix functions and \hat V^{(s)}\hat \alpha_j=(-1}^s\hat \alpha_j\hat V^{(s)} for all anticommuting Hermitian matrices $\hat \alpha_j$, $\hat \alpha_j^2=\hat I$, s=0,1.Comment: 17 page

Remarks on a normal subgroup of GA_n

We show that the subgroup generated by locally finite polynomial automorphisms of k^n is normal in GA_n. Also, some properties of normal subgroups of GA_n containing all diagonal automorphisms are given.Comment: 5 page

Circular photon drag effect in bulk tellurium

The circular photon drag effect is observed in a bulk semiconductor. The photocurrent caused by a transfer of both translational and angular momenta of light to charge carriers is detected in tellurium in the mid-infrared frequency range. Dependencies of the photocurrent on the light polarization and on the incidence angle agree with the symmetry analysis of the circular photon drag effect. Microscopic models of the effect are developed for both intra- and inter-subband optical absorption in the valence band of tellurium. The shift contribution to the circular photon drag current is calculated. An observed decrease of the circular photon drag current with increase of the photon energy is explained by the theory for inter-subband optical transitions. Theoretical estimates of the circular photon drag current agree with the experimental data.Comment: 8 pages, 4 figure

Radio-frequency Bloch-transistor electrometer

A quantum-limited electrometer based on charge modulation of the Josephson supercurrent in the Bloch transistor inserted into a superconducting ring is proposed. As this ring is inductive coupled to a high-Q resonance tank circuit, the variations of the charge on the transistor island (input signal) are converted into variations of amplitude and phase of radio-frequency oscillations in the tank. These variations are amplified and then detected. The output noise, the back-action fluctuations and their cross-correlation are computed. It is shown that our device enables measurements of the charge with a sensitivity which is determined by the energy resolution of its amplifier, that can be reduced down to the standard quantum limit of \hbar/2. On the basis of this setup a "back-action-evading" scheme of the charge measurements is proposed.Comment: 5 pages incl. 2 figure

Differential Form of the Skornyakov--Ter-Martirosyan Equations

The Skornyakov--Ter-Martirosyan three-boson integral equations in momentum space are transformed into differential equations. This allows us to take into account quite directly the Danilov condition providing self-adjointness of the underlying three-body Hamiltonian with zero-range pair interactions. For the helium trimer the numerical solutions of the resulting differential equations are compared with those of the Faddeev-type AGS equations.Comment: 4 pages, 2 figure

Effects of quasiparticle tunneling in a circuit-QED realization of a strongly driven two-level system

We experimentally and theoretically study the frequency shift of a driven cavity coupled to a superconducting charge qubit. In addition to previous studies, we here also consider drive strengths large enough to energetically allow for quasiparticle creation. Quasiparticle tunneling leads to the inclusion of more than two charge states in the dynamics. To explain the observed effects, we develop a master equation for the microwave dressed charge states, including quasiparticle tunneling. A bimodal behavior of the frequency shift as a function of gate voltage can be used for sensitive charge detection. However, at weak drives the charge sensitivity is significantly reduced by non-equilibrium quasiparticles, which induce transitions to a non-sensitive state. Unexpectedly, at high enough drives, quasiparticle tunneling enables a very fast relaxation channel to the sensitive state. In this regime, the charge sensitivity is thus robust against externally injected quasiparticles and the desired dynamics prevail over a broad range of temperatures. We find very good agreement between theory and experiment over a wide range of drive strengths and temperatures.Comment: 25 pages, 7 figure

Global in Time Solutions to Kolmogorov-Feller Pseudodifferential Equations with Small Parameter

The goal in this paper is to demonstrate a new method for constructing global-in-time approximate (asymptotic) solutions of (pseudodifferential) parabolic equations with a small parameter. We show that, in the leading term, such a solution can be constructed by using characteristics, more precisely, by using solutions of the corresponding Hamiltonian system and without using any integral representation. For completeness, we also briefly describe the well-known scheme developed by V.P.Maslov for constructing global-in-time solutions.Comment: 27 page