Level Splitting in Association with the Multiphoton Bloch-Siegert Shift

We present a unitary equivalent spin-boson Hamiltonian in which terms can be identified which contribute to the Bloch-Siegert shift, and to the level splittings at the anticrossings associated with the Bloch-Siegert resonances. First-order degenerate perturbation theory is used to develop approximate results in the case of moderate coupling for the level splitting.Comment: 8 pages, 2 figure

Multiphoton Bloch-Siegert shifts and level-splittings in spin-one systems

We consider a spin-boson model in which a spin 1 system is coupled to an oscillator. A unitary transformation is applied which allows a separation of terms responsible for the Bloch-Siegert shift, and terms responsible for the level splittings at anticrossings associated with Bloch-Siegert resonances. When the oscillator is highly excited, the system can maintain resonance for sequential multiphoton transitions. At lower levels of excitation, resonance cannot be maintained because energy exchange with the oscillator changes the level shift. An estimate for the critical excitation level of the oscillator is developed.Comment: 14 pages, 3 figure

Excitation transfer in two two-level systems coupled to an oscillator

We consider a generalization of the spin-boson model in which two different two-level systems are coupled to an oscillator, under conditions where the oscillator energy is much less than the two-level system energies, and where the oscillator is highly excited. We find that the two-level system transition energy is shifted, producing a Bloch-Siegert shift in each two-level system similar to what would be obtained if the other were absent. At resonances associated with energy exchange between a two-level system and the oscillator, the level splitting is about the same as would be obtained in the spin-boson model at a Bloch-Siegert resonance. However, there occur resonances associated with the transfer of excitation between one two-level system and the other, an effect not present in the spin-boson model. We use a unitary transformation leading to a rotated system in which terms responsible for the shift and splittings can be identified. The level splittings at the anticrossings associated with both energy exchange and excitation transfer resonances are accounted for with simple two-state models and degenerate perturbation theory using operators that appear in the rotated Hamiltonian.Comment: 26 pages, 4 figure

The two phase diagrams for PdD

Abstract only.The phase diagram of PdH (and also PdD) has been studied extensively over the past century or more, and is considered to be well understood. However, there is a subtle issue in connection with the phase diagram this is not well understood; this has to do with the stability of the lattice itself, in connection with the different phases. In the literature, one usually finds the phase diagram for conditions under which the Pd sub-lattice is assumed to be fixed. Given the long relaxation time associated with vacancy diffusion under "normal" conditions, the phase diagram that results is very useful

Quantum-coupled single-electron thermal to electric conversion scheme

Thermal to electric energy conversion with thermophotovoltaics relies on radiation emitted by a hot body, which limits the power per unit area to that of a blackbody. Microgap thermophotovoltaics take advantage of evanescent waves to obtain higher throughput, with the power per unit area limited by the internal blackbody, which is n2 higher. We propose that even higher power per unit area can be achieved by taking advantage of thermal fluctuations in the near-surface electric fields. For this, we require a converter that couples to dipoles on the hot side, transferring excitation to promote carriers on the cold side which can be used to drive an electrical load. We analyze the simplest implementation of the scheme, in which excitation transfer occurs between matched quantum dots. Next, we examine thermal to electric conversion with a lossy dielectric (aluminum oxide) hot-side surface layer. We show that the throughput power per unit active area can exceed the n2 blackbody limit with this kind of converter. With the use of small quantum dots, the scheme becomes very efficient theoretically, but will require advances in technology to fabricate

Multiphoton Bloch-Siegert shifts and level-splittings in a three-level system

In previous work we studied the spin-boson model in the multiphoton regime, using a rotation that provides a separation between terms that contribute most of the level energies away from resonance, and terms responsible for the level splittings at the anticrossing. Here, we consider a generalization of the spin-boson model consisting of a three-level system coupled to an oscillator. We construct a similar rotation and apply it to the more complicated model. We find that the rotation provides a useful approximation to the energy levels in the multiphoton region of the new problem. We find that good results can be obtained for the level splittings at the anticrossings for resonances involving the lower two levels in regions away from accidental or low-order resonances of the upper two levels.Comment: 29 pages, 13 figure

DIRECTIONAL SQUARE FUNCTIONS

QuantitativeformulationsofFefferman’scounterexamplefortheballmultiplierare naturally linked to square function estimates for conical and directional multipliers. In this ar- ticle we develop a novel framework for these square function estimates, based on a directional embedding theorem for Carleson sequences and multi-parameter time-frequency analysis tech- niques. As applications we prove sharp or quantified bounds for Rubio de Francia type square functions of conical multipliers and of multipliers adapted to rectangles pointing along di- rections. A suitable combination of these estimates yields a new and currently best-known logarithmic bound for the Fourier restriction to an -gon, improving on previous results of A. Córdoba. Our directional Carleson embedding extends to the weighted setting, yielding previ- ously unknown weighted estimates for directional maximal functions and singular integrals

A new look at low-energy nuclear reaction (LENR) research: a response to Shanahan

In his criticisms of the review article on LENR by Krivit and Marwan, Shanahan has raised a number of issues in the areas of calorimetry, heat after death, elemental transmutation, energetic particle detection using CR-39, and the temporal correlation between heat and helium-4. These issues are addressed by the researchers who conducted the original work that was discussed in the Krivit-Marwan (K&M) review paper

Geometric maximal operators and BMO on product bases

We consider the problem of the boundedness of maximal operators on BMO on shapes in $\mathbb{R}^n$. We prove that for bases of shapes with an engulfing property, the corresponding maximal function is bounded from BMO to BLO, generalising a known result of Bennett for the basis of cubes. When the basis of shapes does not possess an engulfing property but exhibits a product structure with respect to lower-dimensional shapes coming from bases that do possess an engulfing property, we show that the corresponding maximal function is bounded from BMO to a space we define and call rectangular BLO