Eternally non-Markovian dynamics of a qubit interacting with a single-photon wavepacket

An evolution of a two-level system (qubit) interacting with a single-photon wave packet is analyzed. It is shown that a hierarchy of master equations gives rise to phase covariant qubit evolution. The temporal correlations in the input field induce nontrivial memory effects for the evolution of a qubit. It is shown that in the resonant case whenever time-local generator is regular (does not display singularities) the qubit evolution never displays information backflow. However, in general the generator might be highly singular leading to intricate non-Markovian effects. A detailed analysis of the exponential profile is provided which allows to illustrate all characteristic feature of the qubit evolution.

On the Nonlinear Mode-Coupling in Ultra Precision Manufacturing Machines: Experimental and Analytical Analyses

Recent studies in passively-isolated systems have shown that mode coupling is desirable for best vibration suppression, thus refuting the long-standing rule of mode decoupling. However, these studies have ignored the non-linearities in the isolators. In this work, we consider stiffness nonlinearity from pneumatic isolators and study the nonlinear free undamped vibrations of a passively-isolated ultra-precision manufacturing (UPM) machine. Experimental analysis is conducted to guide the mathematical formulation. The system comprises linearly and nonlinearly coupled in-plane horizontal and rotational motion of the UPM machine with quadratic nonlinear stiffness from the isolators. We present closed-form expressions using the method of multiple scales for two cases viz. the non-resonant case and the bounded internal resonance case. We validate our theoretical findings through direct numerical simulations. For the non-resonant case, we show that the system behaves similar to a linear system. However, for the nearly internal resonance case, we demonstrate strong energy exchange between the modes stemming from nonlinear mode coupling. We further study the effect of nonlinear mode coupling on the vibration isolation performance and demonstrate that mode coupling is not always desirable.

Crime, Order and the Two Faces of Conservatism: an Encounter with Criminology’s other

Over the past half century, conservatism has been a powerful force in shaping public and political responses to crime in Britain. But within criminology, conservative ideology remains curiously neglected and poorly understood. In this paper, I develop an interpretive reconstruction of conservative thinking about crime that seeks to make good this inattention. My central contention is that one finds in conservative ideology both an emotionally and culturally resonant case for making police authority and penal control central to the production of order and arguments for sceptical penal restraint and non-penal modes of socialization. But from which aspects of its conceptual morphology do these two faces of conservatism arise? In answering this question, my encounter identifies the claims that conservatism brings to contests over a better politics of crime (claims with which non-conservatives are required to reckon), as well as pinpointing certain shortcomings and blind spots of conservative ideology.

Approximate cloaking for electromagnetic waves via transformation optics: Cloaking versus infinite energy

We study the approximate cloaking via transformation optics for electromagnetic waves in the time harmonic regime in which the cloaking device only consists of a layer constructed by the mapping technique. Due to the fact that no-lossy layer is required, resonance might appear and the analysis is delicate. We analyze both non-resonant and resonant cases. In particular, we show that the energy can blow up inside the cloaked region in the resonant case and/whereas cloaking is achieved in both cases. Moreover, the degree of visibility depends on the compatibility of the source inside the cloaked region and the system. These facts are new and distinct from known mathematical results in the literature.

Groundstates for Choquard type equations with Hardy–Littlewood–Sobolev lower critical exponent

For the Choquard equation, which is a nonlocal nonlinear Schrödinger type equation, $$-\Delta u+V_{\mu, \nu} u=(I_\alpha\ast \vert u \vert ^{({N+\alpha})/{N}}){ \vert u \vert }^{{\alpha}/{N}-1}u,\quad {\rm in} \ {\open R}^N, $$where $N\ges 3$, Vμ,ν :ℝN → ℝ is an external potential defined for μ, ν > 0 and x ∈ ℝN by Vμ,ν(x) = 1 − μ/(ν2 + |x|2) and $I_\alpha : {\open R}^N \to 0$ is the Riesz potential for α ∈ (0, N), we exhibit two thresholds μν, μν > 0 such that the equation admits a positive ground state solution if and only if μν < μ < μν and no ground state solution exists for μ < μν. Moreover, if μ > max{μν, N2(N − 2)/4(N + 1)}, then equation still admits a sign changing ground state solution provided $N \ges 4$ or in dimension N = 3 if in addition 3/2 < α < 3 and $\ker (-\Delta + V_{\mu ,\nu }) = \{ 0\} $, namely in the non-resonant case.