Dirac Quantization of the Pais-Uhlenbeck Fourth Order Oscillator

As a model, the Pais-Uhlenbeck fourth order oscillator with equation of motion $d^4q/dt^4+(\omega_1^2+\omega_2^2)d^2q/dt^2 +\omega_1^2\omega_2^2 q=0$ is a quantum-mechanical prototype of a field theory containing both second and fourth order derivative terms. With its dynamical degrees of freedom obeying constraints due to the presence of higher order time derivatives, the model cannot be quantized canonically. We thus quantize it using the method of Dirac constraints to construct the correct quantum-mechanical Hamiltonian for the system, and find that the Hamiltonian diagonalizes in the positive and negative norm states that are characteristic of higher derivative field theories. However, we also find that the oscillator commutation relations become singular in the $\omega_1 \to \omega_2$ limit, a limit which corresponds to a prototype of a pure fourth order theory. Thus the particle content of the $\omega_1 =\omega_2$ theory cannot be inferred from that of the $\omega_1 \neq \omega_2$ theory; and in fact in the $\omega_1 \to \omega_2$ limit we find that all of the $\omega_1 \neq \omega_2$ negative norm states move off shell, with the spectrum of asymptotic in and out states of the equal frequency theory being found to be completely devoid of states with either negative energy or negative norm. As a byproduct of our work we find a Pais-Uhlenbeck analog of the zero energy theorem of Boulware, Horowitz and Strominger, and show how in the equal frequency Pais-Uhlenbeck theory the theorem can be transformed into a positive energy theorem instead.Comment: RevTeX4, 20 pages. Final version, to appear in Phys. Rev.

The clash of symmetries in a Randall-Sundrum-like spacetime

We present a toy model that exhibits clash-of-symmetries style Higgs field kink configurations in a Randall-Sundrum-like spacetime. The model has two complex scalar fields Phi_{1,2}, with a sextic potential obeying global U(1)xU(1) and discrete Phi_1 Phi_2 interchange symmetries. The scalar fields are coupled to 4+1 dimensional gravity endowed with a bulk cosmological constant. We show that the coupled Einstein-Higgs field equations have an interesting analytic solution provided the sextic potential adopts a particular form. The 4+1 metric is shown to be that of a smoothed-out Randall-Sundrum type of spacetime. The thin-brane Randall-Sundrum limit, whereby the Higgs field kinks become step functions, is carefully defined in terms of the fundamental parameters in the action. The ``clash of symmetries'' feature, defined in previous papers, is manifested here through the fact that both of the U(1) symmetries are spontaneously broken at all non-asymptotic points in the extra dimension $w$. One of the U(1)'s is asymptotically restored as w --> -infinity, with the other U(1) restored as w --> +infinity. The spontaneously broken discrete symmetry ensures topological stability. In the gauged version of this model we find new flat-space solutions, but in the warped metric case we have been unable to find any solutions with nonzero gauge fields.Comment: 15 pages, 5 figures; minor changes including added references and an updated figure; to appear in Phys Rev

The approach to a superconductor-to-Bose-insulator transition in disordered films

Through a detailed study of scaling near the magnetic field-tuned superconductor-to-insulator transition in strongly disordered films, we find that results for a variety of materials can be collapsed onto a single phase diagram. The data display two clear branches, one with weak disorder and an intervening metallic phase, the other with strong disorder. Along the strongly disordered branch, the resistance at the critical point approaches $R_Q = h/4e^2$ and the scaling of the resistance is consistent with quantum percolation, and therefore with the predictions of the dirty boson model.Comment: 4 pages, 4 figure

Quantum advantages in classically defined tasks

We analyze classically defined games for which a quantum team has an advantage over any classical team. The quantum team has a clear advantage in games in which the players of each team are separated in space and the quantum team can use unusually strong correlations of the Einstein-Podolsky-Rosen (EPR) type. We present an example of a classically defined game played at one location for which quantum players have a real advantage.Comment: 4 pages, revised version, to be published in PR

Nonlinear Induction Detection of Electron Spin Resonance

We present a new approach to the induction detection of electron spin resonance (ESR) signals exploiting the nonlinear properties of a superconducting resonator. Our experiments employ a yttrium barium copper oxide (YBCO) superconducting stripline microwave (MW) resonator integrated with a microbridge. A strong nonlinear response of the resonator is thermally activated in the microbridge when exceeding a threshold in the injected MW power. The responsivity factor characterizing the ESR-induced change in the system's output signal is about 100 times larger when operating the resonator near the instability threshold, compared to the value obtained in the linear regime of operation. Preliminary experimental results, together with a theoretical model of this phenomenon are presented. Under appropriate conditions nonlinear induction detection of ESR can potentially improve upon the current capabilities of conventional linear induction detection ESR

SU(5) grand unification on a domain-wall brane from an E_6-invariant action

An SU(5) grand unification scheme for effective 3+1-dimensional fields dynamically localised on a domain-wall brane is constructed. This is achieved through the confluence of the clash-of-symmetries mechanism for symmetry breaking through domain-wall formation, and the Dvali-Shifman gauge-boson localisation idea. It requires an E_6 gauge-invariant action, yielding a domain-wall solution that has E_6 broken to differently embedded SO(10) x U(1) subgroups in the two bulk regions on opposite sides of the wall. On the wall itself, the unbroken symmetry is the intersection of the two bulk subgroups, and contains SU(5). A 4+1-dimensional fermion family in the 27 of E_6 gives rise to localised left-handed zero-modes in the 5^* + 10 + 1 + 1 representation of SU(5). The remaining ten fermion components of the 27 are delocalised exotic states, not appearing in the effective 3+1-dimensional theory on the domain-wall brane. The scheme is compatible with the type-2 Randall-Sundrum mechanism for graviton localisation; the single extra dimension is infinite.Comment: 21 pages, 9 figures. Minor changes to text and references. To appear in Phys. Rev.