Riccati parameter modes from Newtonian free damping motion by supersymmetry

We determine the class of damped modes \tilde{y} which are related to the common free damping modes y by supersymmetry. They are obtained by employing the factorization of Newton's differential equation of motion for the free damped oscillator by means of the general solution of the corresponding Riccati equation together with Witten's method of constructing the supersymmetric partner operator. This procedure leads to one-parameter families of (transient) modes for each of the three types of free damping, corresponding to a particular type of %time-dependent angular frequency. %time-dependent, antirestoring acceleration (adding up to the usual Hooke restoring acceleration) of the form a(t)=\frac{2\gamma ^2}{(\gamma t+1)^{2}}\tilde{y}, where \gamma is the family parameter that has been chosen as the inverse of the Riccati integration constant. In supersymmetric terms, they represent all those one Riccati parameter damping modes having the same Newtonian free damping partner modeComment: 6 pages, twocolumn, 6 figures, only first 3 publishe

Self-adjoint Time Operator is the Rule for Discrete Semibounded Hamiltonians

We prove explicitly that to every discrete, semibounded Hamiltonian with constant degeneracy and with finite sum of the squares of the reciprocal of its eigenvalues and whose eigenvectors span the entire Hilbert space there exists a characteristic self-adjoint time operator which is canonically conjugate to the Hamiltonian in a dense subspace of the Hilbert space. Moreover, we show that each characteristic time operator generates an uncountable class of self- adjoint operators canonically conjugate with the same Hamiltonian in the same dense subspace.Comment: accepted for publication in the Proceedings of the Royal Society of London

Proposal to demonstrate the non-locality of Bohmian mechanics with entangled photons

Bohmian mechanics reproduces all statistical predictions of quantum mechanics, which ensures that entanglement cannot be used for superluminal signaling. However, individual Bohmian particles can experience superluminal influences. We propose to illustrate this point using a double double-slit setup with path-entangled photons. The Bohmian velocity field for one of the photons can be measured using a recently demonstrated weak-measurement technique. The found velocities strongly depend on the value of a phase shift that is applied to the other photon, potentially at spacelike separation.Comment: 6 pages, 4 figure

Quantum Optics

Quantum optics, i.e. the interaction of individual photons with matter, began with the discoveries of Planck and Einstein, but in recent years it has expanded beyond pure physics to become an important driving force for technological innovation. This book serves the broader readership growing out of this development by starting with an elementary description of the underlying physics and then building up a more advanced treatment. The reader is led from the quantum theory of thesimple harmonic oscillator to the application of entangled states to quantum information processing. An equally impo

Pauli's Theorem and Quantum Canonical Pairs: The Consistency Of a Bounded, Self-Adjoint Time Operator Canonically Conjugate to a Hamiltonian with Non-empty Point Spectrum

In single Hilbert space, Pauli's well-known theorem implies that the existence of a self-adjoint time operator canonically conjugate to a given Hamiltonian signifies that the time operator and the Hamiltonian possess completely continuous spectra spanning the entire real line. Thus the conclusion that there exists no self-adjoint time operator conjugate to a semibounded or discrete Hamiltonian despite some well-known illustrative counterexamples. In this paper we evaluate Pauli's theorem against the single Hilbert space formulation of quantum mechanics, and consequently show the consistency of assuming a bounded, self-adjoint time operator canonically conjugate to a Hamiltonian with an unbounded, or semibounded, or finite point spectrum. We point out Pauli's implicit assumptions and show that they are not consistent in a single Hilbert space. We demonstrate our analysis by giving two explicit examples. Moreover, we clarify issues sorrounding the different solutions to the canonical commutation relations, and, consequently, expand the class of acceptable canonical pairs beyond the solutions required by Pauli's theorem.Comment: contains corrections to minor typographical errors of the published versio

Phosphorus limitation of aboveground production in northern hardwood forests

Forest productivity on glacially derived soils with weatherable phosphorus (P) is expected to be limited by nitrogen (N), according to theories of long-term ecosystem development. However, recent studies and model simulations based on resource optimization theory indicate that productivity can be co-limited by N and P. We conducted a full factorial N × P fertilization experiment in 13 northern hardwood forest stands of three age classes in central New Hampshire, USA, to test the hypothesis that forest productivity is co-limited by N and P. We also asked whether the response of productivity to N and P addition differs among species and whether differential species responses contribute to community-level co-limitation. Plots in each stand were fertilized with 30 kg N·ha−1·yr−1, 10 kg P·ha−1·yr−1, N + P, or neither nutrient (control) for four growing seasons. The productivity response to treatments was assessed using per-tree annual relative basal area increment (RBAI) as an index of growth. RBAI responded significantly to P (P = 0.02) but not to N (P = 0.73). However, evidence for P limitation was not uniform among stands. RBAI responded to P fertilization in mid-age (P = 0.02) and mature (P = 0.07) stands, each taken as a group, but was greatest in N-fertilized plots of two stands in these age classes, and there was no significant effect of P in the young stands. Both white birch (Betula papyrifera Marsh.) and beech (Fagus grandifolia Ehrh.) responded significantly to P; no species responded significantly to N. We did not find evidence for N and P co-limitation of tree growth. The response to N + P did not differ from that to P alone, and there was no significant N × P interaction (P = 0.68). Our P limitation results support neither the N limitation prediction of ecosystem theory nor the N and P co-limitation prediction of resource optimization theory, but could be a consequence of long-term anthropogenic N deposition in these forests. Inconsistencies in response to P suggest that successional status and variation in site conditions influence patterns of nutrient limitation and recycling across the northern hardwood forest landscape

Deterministic Generation of Entangled Photons in Superconducting Resonator Arrays

We present a scheme for the deterministic generation of entangled photon pairs in a superconducting resonator array. The resonators form a Jaynes-Cummings lattice via the coupling to superconducting qubits, and the Kerr-like nonlinearity arises due to the coupling.We show that entangled photons can be generated on demand by applying spectroscopic techniques and exploiting the nonlinearity and symmetry in the resonators. The scheme is robust against small parameter spreads due to fabrication errors. Our findings can be used as a key element for quantum information processing in superconducting quantum circuits.Comment: 4 pages, 3 figure