A proof of the Kramers degeneracy of transmission eigenvalues from antisymmetry of the scattering matrix

In time reversal symmetric systems with half integral spins (or more concretely, systems with an antiunitary symmetry that squares to -1 and commutes with the Hamiltonian) the transmission eigenvalues of the scattering matrix come in pairs. We present a proof of this fact that is valid both for even and odd number of modes and relies solely on the antisymmetry of the scattering matrix imposed by time reversal symmetry.Comment: 2 page

Insight into Resonant Activation in Discrete Systems

The resonant activation phenomenon (RAP) in a discrete system is studied using the master equation formalism. We show that the RAP corresponds to a non-monotonic behavior of the frequency dependent first passage time probability density function (pdf). An analytical expression for the resonant frequency is introduced, which, together with numerical results, helps understand the RAP behavior in the space spanned by the transition rates for the case of reflecting and absorbing boundary conditions. The limited range of system parameters for which the RAP occurs is discussed. We show that a minimum and a maximum in the mean first passage time (MFPT) can be obtained when both boundaries are absorbing. Relationships to some biological systems are suggested.Comment: 5 pages, 5 figures, Phys. Rev. E., in pres

Storage of classical information in quantum spins

Digital magnetic recording is based on the storage of a bit of information in the orientation of a magnetic system with two stable ground states. Here we address two fundamental problems that arise when this is done on a quantized spin: quantum spin tunneling and back-action of the readout process. We show that fundamental differences exist between integer and semi-integer spins when it comes to both, read and record classical information in a quantized spin. Our findings imply fundamental limits to the miniaturization of magnetic bits and are relevant to recent experiments where spin polarized scanning tunneling microscope reads and records a classical bit in the spin orientation of a single magnetic atom

Activated escape of periodically modulated systems

The rate of noise-induced escape from a metastable state of a periodically modulated overdamped system is found for an arbitrary modulation amplitude $A$. The instantaneous escape rate displays peaks that vary with the modulation from Gaussian to strongly asymmetric. The prefactor $\nu$ in the period-averaged escape rate depends on $A$ nonmonotonically. Near the bifurcation amplitude $A_c$ it scales as $\nu\propto (A_c-A)^{\zeta}$. We identify three scaling regimes, with $\zeta = 1/4, -1$, and 1/2

Low-Temperature Properties of Two-Dimensional Ideal Ferromagnets

The manifestation of the spin-wave interaction in the low-temperature series of the partition function has been investigated extensively over more than seven decades in the case of the three-dimensional ferromagnet. Surprisingly, the same problem regarding ferromagnets in two spatial dimensions, to the best of our knowledge, has never been addressed in a systematic way so far. In the present paper the low-temperature properties of two-dimensional ideal ferromagnets are analyzed within the model-independent method of effective Lagrangians. The low-temperature expansion of the partition function is evaluated up to two-loop order and the general structure of this series is discussed, including the effect of a weak external magnetic field. Our results apply to two-dimensional ideal ferromagnets which exhibit a spontaneously broken spin rotation symmetry O(3) $\to$ O(2) and are defined on a square, honeycomb, triangular or Kagom\'e lattice. Remarkably, the spin-wave interaction only sets in at three-loop order. In particular, there is no interaction term of order $T^3$ in the low-temperature series for the free energy density. This is the analog of the statement that, in the case of three-dimensional ferromagnets, there is no interaction term of order $T^4$ in the free energy density. We also provide a careful discussion of the implications of the Mermin-Wagner theorem in the present context and thereby put our low-temperature expansions on safe grounds.Comment: 24 pages, 3 figure

Strong Orientation Effects in Ionization of H2+_2^+ by Short, Intense, High-Frequency Light Sources

We present three dimensional time-dependent calculations of ionization of arbitrarily spatially oriented H$_2^+$ by attosecond, intense, high-frequency laser fields. The ionization probability shows a strong dependence on both the internuclear distance and the relative orientation between the laser field and the internuclear axis.Comment: 4 pages, 4 figure

Time Reversal and n-qubit Canonical Decompositions

For n an even number of qubits and v a unitary evolution, a matrix decomposition v=k1 a k2 of the unitary group is explicitly computable and allows for study of the dynamics of the concurrence entanglement monotone. The side factors k1 and k2 of this Concurrence Canonical Decomposition (CCD) are concurrence symmetries, so the dynamics reduce to consideration of the a factor. In this work, we provide an explicit numerical algorithm computing v=k1 a k2 for n odd. Further, in the odd case we lift the monotone to a two-argument function, allowing for a theory of concurrence dynamics in odd qubits. The generalization may also be studied using the CCD, leading again to maximal concurrence capacity for most unitaries. The key technique is to consider the spin-flip as a time reversal symmetry operator in Wigner's axiomatization; the original CCD derivation may be restated entirely in terms of this time reversal. En route, we observe a Kramers' nondegeneracy: the existence of a nondegenerate eigenstate of any time reversal symmetric n-qubit Hamiltonian demands (i) n even and (ii) maximal concurrence of said eigenstate. We provide examples of how to apply this work to study the kinematics and dynamics of entanglement in spin chain Hamiltonians.Comment: 20 pages, 3 figures; v2 (17pp.): major revision, new abstract, introduction, expanded bibliograph

Noise activated granular dynamics

We study the behavior of two particles moving in a bistable potential, colliding inelastically with each other and driven by a stochastic heat bath. The system has the tendency to clusterize, placing the particles in the same well at low drivings, and to fill all of the available space at high temperatures. We show that the hopping over the potential barrier occurs following the Arrhenius rate, where the heat bath temperature is replaced by the granular temperature. Moreover, within the clusterized ``phase'' one encounters two different scenarios: for moderate inelasticity, the jumps from one well to the other involve one particle at a time, whereas for strong inelasticity the two particles hop simultaneously.Comment: RevTex4, 4 pages, 4 eps figures, Minor revisio

Recurrent difficulties: solving quantitative problems

Investigating the process students use to solve quantitative problems using a think aloud strategy