Quantum jumps between Fock states of a one-electron oscillator reveal the quantum limit of a cyclotron. With a surrounding cavity inhibiting synchrotron radiation 140-fold, the jumps show a 13 s Fock state lifetime and a cyclotron in thermal equilibrium with 1.6 to 4.2 K blackbody photons. These disappear by 80 mK, a temperature 50 times lower than previously achieved with an isolated elementary particle. The cyclotron stays in its ground state until a resonant photon is injected. A quantum cyclotron offers a new route to measuring the electron magnetic moment and the fine structure constant.

A Comment on the Letter by Stefano Zapperi, et al., Phys. Rev. Lett. 78, 1408 (1997). The authors of the Letter offer a Reply.

A Reply to the Comment by G. Caldarelli and A. Petri.

A Comment on the Letter by Gregory L. Baker, James A. Blackburn, and H. J. T. Smith, Phys. Rev. Lett. 81, 554 (1998). The authors of the Letter offer a Reply.

A Reply to the Comment by P. Muruganandam, S. Parthasarathy, and M. Lakshmanan.

A Comment on the Letter by Carlo Rovelli. Phys. Rev. Lett. 80, 4613 (1998). The authors of the Letter offer a Reply.

A reply to the Comment by N. P. Landsman.

The lifetime of a Bloch particle in a homogeneous field is calculated numerically as a function of the field amplitude. A simple model explaining the characteristic features of the field dependence of the lifetime is introduced. The theoretical results are compared with the experimental data of C. F. Bharucha et al. [Phys. Rev. A 55, R857 (1997)] obtained for cold sodium atoms in an accelerated optical lattice.

Simulations of a rotationally stirred condensate show that a regime of simple behavior occurs in which a single vortex cycles in and out of the condensate. We present a simple quantitative model of this behavior, which accurately describes the full vortex dynamics, including a critical angular speed of stirring for vortex formation. A method for experimentally preparing a condensate in a central vortex state is suggested.

Fluctuation-induced switching of driven bistable systems, far from equilibrium, has been the focus of theoretical analysis and analog circuit computations. A parametrically driven electron in a Penning trap is shown to be a nearly ideal experimental realization. Noise applied to this dynamic double well system produces random switching between two steady-state oscillations which differ in the oscillation phase by ${180}^{\circ }$.

We generalize the definition of the energy output of an engine as the minimum energy input required to accomplish the same task as the engine. Applying this new concept to molecular motors makes it possible to measure their efficiency even without attaching any external load to them. This way we can compare and characterize the operation of molecular motors in various situations. We also investigate how the thermally driven motors differ from other motors.

Quantum tunneling was observed in the decay of metastable spin domains in gaseous Bose-Einstein condensates. A mean-field description of the tunneling was developed and compared with measurement. The tunneling rates are a sensitive probe of the boundary between spin domains, and indicate a spin structure which is prohibited in the bulk fluid. These experiments were performed with optically trapped $F=1\mathrm{}$ spinor Bose-Einstein condensates of sodium.

The angle-angular momentum entropic upper bounds are proved in a more general form by using Tsallis-like entropies for the quantum scattering of the spinless particles. So, the problem to find an upper bound for all Tsallis-like scattering entropy when the elastic integrated cross section ${\sigma }_{\mathrm{el}}$ and the forward differential cross section $\frac{d\sigma }{d\Omega }\left(1\right)$ are fixed is completely solved in terms of the optimal entropies obtained from the principle of minimum distance in the space of states. The results on experimental tests of these optimal upper bounds are presented for both extensive and nonextensive statistics cases.

We consider a single particle which is bound by a central potential and obeys the Dirac equation. We compare two cases, $a$ and $b$, in which the masses are the same but $V_a<V_b$, where $V$ is the time component of a vector potential. We prove generally that for each discrete eigenvalue $E$ whose corresponding (large and small) radial wave functions have no nodes, it necessarily follows that $E_a<E_b$. As an illustration, this general relativistic comparison theorem is applied to approximate the Dirac spectrum generated by a screened-Coulomb potential.

Long-range frustrating interactions, even if their strength is infinitesimal, can give rise to a dramatic proliferation of ground or near-ground states. As a consequence, the ordering temperature can exhibit a discontinuous drop as a function of the frustration. We have found this phenomenon in an entire class of models: amphiphilic systems, Mott insulators, and gauge theories of metallic glasses, to name a few.

As far as entanglement is concerned, two density matrices of $n$ particles are completely equivalent if one can be transformed into the other by local unitary transformations. We present two methods to find whether or not two generic density matrices of arbitrary numbers of spin-1/2 particles are equivalent. Both methods describe density matrices in terms of a finite number of invariant parameters.

We construct lattice Hamiltonians with homogeneous interaction potentials which allow for explicit breather solutions. Especially we obtain exponentially localized solutions for $d$-dimensional lattices with $d=2,3\mathrm{}$.

A symmetric dissipative two-state system is asymptotically completely delocalized independent of the initial state. We show that driving-induced localization at long times can take place when both the bias and tunneling coupling energy are harmonically modulated. Dynamical symmetry breaking on average occurs when the driving frequencies are odd multiples of some reference frequency. This effect is universal, as it is independent of the dissipative mechanism. Possible candidates for an experimental observation are flux tunneling in the variable barrier rf SQUID and magnetization tunneling in magnetic molecular clusters.

We point out that using the state-of-the-art (or soon-to-be) intense electromagnetic pulses, violent accelerations that may be suitable for testing quantum field theory in curved spacetime can be realized through the interaction of a high-intensity laser with an electron. In particular, we demonstrate that the Unruh radiation is detectable, in principle, beyond the conventional radiation (most notably the Larmor radiation) background noise, by taking advantage of its specific dependence on the laser power and distinct character in spectral-angular distributions.

We extend the use of Bell inequalities to $\Phi \to K^0{\overline{K}}^0$ decays by exploiting analogies and differences to the well-known and experimentally verified singlet-spin case. Contrasting with other analyses, our Bell inequalities are violated by quantum mechanics and can strictly be derived from local realistic theories. In principle, quantum mechanics could then be tested using unstable, oscillating states governed by a $\mathrm{CP}-\mathrm{violating}$ Hamiltonian.