Observing the Spontaneous Breakdown of Unitarity

During the past decade, the experimental development of being able to create ever larger and heavier quantum superpositions has brought the discussion of the connection between microscopic quantum mechanics and macroscopic classical physics back to the forefront of physical research. Under equilibrium conditions this connection is in fact well understood in terms of the mechanism of spontaneous symmetry breaking, while the emergence of classical dynamics can be described within an ensemble averaged description in terms of decoherence. The remaining realm of individual-state quantum dynamics in the thermodynamic limit was addressed in a recent paper proposing that the unitarity of quantum mechanical time evolution in macroscopic objects may be susceptible to a spontaneous breakdown. Here we will discuss the implications of this theory of spontaneous unitarity breaking for the modern experiments involving truly macroscopic Schrodinger cat states.Comment: 4 pages, no figure

An instability of unitary quantum dynamics

Instabilities of equilibrium quantum mechanics are common and well-understood. They are manifested for example in phase transitions, where a quantum system becomes so sensitive to perturbations that a symmetry can be spontaneously broken. Here, we consider the possibility that the time evolution governing quantum dynamics may be similarly subject to an instability, at which its unitarity spontaneously breaks down owing to an extreme sensitivity towards perturbations. We find that indeed such an instability exists, and we explore its immediate consequences. Interpretations of the results both in terms of extreme sensitivity to the influence of environmental degrees of freedom, and in terms of a possible fundamental violation of unitarity are discussed.Comment: 11 pages, 2 figures; Conference proceedings DICE 201

Quantum Dynamics in the Thermodynamic Limit

The description of spontaneous symmetry breaking that underlies the connection between classically ordered objects in the thermodynamic limit and their individual quantum mechanical building blocks is one of the cornerstones of modern condensed matter theory and has found applications in many different areas of physics. The theory of spontaneous symmetry breaking however, is inherently an equilibrium theory, which does not address the dynamics of quantum systems in the thermodynamic limit. Here, we will use the example of a particular antiferromagnetic model system to show that the presence of a so-called thin spectrum of collective excitations with vanishing energy -one of the well-known characteristic properties shared by all symmetry-breaking objects- can allow these objects to also spontaneously break time-translation symmetry in the thermodynamic limit. As a result, that limit is found to be able, not only to reduce quantum mechanical equilibrium averages to their classical counterparts, but also to turn individual-state quantum dynamics into classical physics. In the process, we find that the dynamical description of spontaneous symmetry breaking can also be used to shed some light on the possible origins of Born's rule. We conclude by describing an experiment on a condensate of exciton polaritons which could potentially be used to experimentally test the proposed mechanism.Comment: 13 pages, 4 figures; typos corrected, references updated, minor changes in tex

Comment on "Charge-parity symmetry observed through Friedel oscillations in chiral charge-density waves" by J. Ishioka et al

In their publication [Phys. Rev B, 84, 245125 (2011)], Ishioka et al. discuss the recently discovered chiral charge density wave state in 1T-TiSe2 in terms of a parameter H_CDW, whose sign is suggested to correspond to the handedness of the chiral order. Here we point out that H_CDW, as defined by Ishioka et al., cannot be used to characterize chirality in that way. An alternative measure of chirality for the specific case of 1T-TiSe2 is suggested

Broken Time Translation Symmetry as a model for Quantum State Reduction

The symmetries that govern the laws of nature can be spontaneously broken, enabling the occurrence of ordered states. Crystals arise from the breaking of translation symmetry, magnets from broken spin rotation symmetry and massive particles break a phase rotation symmetry. Time translation symmetry can be spontaneously broken in exactly the same way. The order associated with this form of spontaneous symmetry breaking is characterised by the emergence of quantum state reduction: systems which spontaneously break time translation symmetry act as ideal measurement machines. In this review the breaking of time translation symmetry is first compared to that of other symmetries such as spatial translations and rotations. It is then discussed how broken time translation symmetry gives rise to the process of quantum state reduction and how it generates a pointer basis, Born's rule, etc. After a comparison between this model and alternative approaches to the problem of quantum state reduction, the experimental implications and possible tests of broken time translation symmetry in realistic experimental settings are discussed.Comment: 15 pages, 5 figure

Optical Gyrotropy and the Nonlocal Hall Effect in Chiral Charge Ordered TiSe2_2

It has been suggested that materials which break spatial inversion symmetry, but not time reversal symmetry, will be optically gyrotropic and display a nonlocal Hall effect. The associated optical rotary power and the suggested possibility of inducing a Kerr effect in such materials, in turn are central to recent discussions about the nature of the pseudogap phases of various cuprate high-temperature superconductors. In this letter, we show that optical gyrotropy and the nonlocal Hall effect provide a sensitive probe of broken inversion symmetry in $1T$-TiSe$_2$. This material was recently found to possess a chiral charge ordered phase at low temperatures, in which inversion symmetry is spontaneously broken, while time reversal symmetry remains unbroken throughout its phase diagram. We estimate the magnitude of the resulting gyrotropic constant and optical rotary power and suggest that $1T$-TiSe$_2$ may be employed as a model material in the interpretation of recent Kerr effect measurements in cuprate superconductors.Comment: 5 pages, 3 figure

Conditions for superdecoherence

Decoherence is the main obstacle to quantum computation. The decoherence rate per qubit is typically assumed to be constant. It is known, however, that quantum registers coupling to a single reservoir can show a decoherence rate per qubit that increases linearly with the number of qubits. This effect has been referred to as superdecoherence, and has been suggested to pose a threat to the scalability of quantum computation. Here, we show that superdecoherence is absent when the spectrum of the single reservoir is continuous, rather than discrete. The reason of this absence, is that, as the number of qubits is increased, a quantum register inevitably becomes susceptible to an ever narrower bandwidth of frequencies in the reservoir. Furthermore, we show that for superdecoherence to occur in a reservoir with a discrete spectrum, one of the frequencies in the reservoir has to coincide exactly with the frequency the quantum register is most susceptible to. We thus fully resolve the conditions that determine the presence or absence of superdecoherence. We conclude that superdecoherence is easily avoidable in practical realizations of quantum computers.Comment: 20 pages, 6 figures, quantum journal accepted versio

Dynamical fidelity susceptibility of decoherence-free subspaces

In idealized models of a quantum register and its environment, quantum information can be stored indefinitely by encoding it into a decoherence-free subspace (DFS). Nevertheless, perturbations to the idealized register-environment coupling will cause decoherence in any realistic setting. Expanding a measure for state preservation, the dynamical fidelity, in powers of the strength of the perturbations, we prove stability to linear order is a generic property of quantum state evolution. The effect of noise perturbation is quantified by a concise expression for the strength of the quadratic, leading order, which we define as the dynamical fidelity susceptibility of DFSs. Under the physical restriction that noise acts on the register $k$-locally, this susceptibility is bounded from above by a polynomial in the system size. These general results are illustrated by two physically relevant examples. Knowledge of the susceptibility can be used to increase coherence times of future quantum computers.Comment: 10 pages, 0 figures, corrected typos, section added, changed notatio

Charge Ordering Geometries in Uniaxially-Strained NbSe2_2

Recent STM experiments reveal niobium diselenide to support domains of striped (1Q) charge order side-by-side with its better-known triangular (3Q) phase, suggesting that small variations in local strain may induce a quantum phase transition between the two. We use a theoretical model of the charge order in NbSe$_2$, based on a strong momentum- and orbital-dependent electron-phonon coupling, to study the effect of uniaxial strain. We find that as little as $0.1\%$ anisotropic shift in phonon energies breaks the threefold symmetry in favor of a 1Q state, in agreement with the experimental results. The altered symmetries change the transition into the ordered state from weakly-first-order in the 3Q case, to second order in the 1Q regime. Modeling the pseudogap phase of NbSe$_2$ as the range of temperatures above the onset of long-range order in which phase coherence is destroyed by local phonon fluctuations, we find a shortening of the local ordering wavevector with increasing temperature, complementing recent X-ray diffraction observations within the low-temperature phase.Comment: 5 pages, 3 figure

Tasks, cognitive agents, and KB-DSS in workflow and process management

The purpose of this paper is to propose a nonparametric interest rate term structure model and investigate its implications on term structure dynamics and prices of interest rate derivative securities. The nonparametric spot interest rate process is estimated from the observed short-term interest rates following a robust estimation procedure and the market price of interest rate risk is estimated as implied from the historical term structure data. That is, instead of imposing a priori restrictions on the model, data are allowed to speak for themselves, and at the same time the model retains a parsimonious structure and the computational tractability. The model is implemented using historical Canadian interest rate term structure data. The parametric models with closed form solutions for bond and bond option prices, namely the Vasicek (1977) and CIR (1985) models, are also estimated for comparison purpose. The empirical results not only provide strong evidence that the traditional spot interest rate models and market prices of interest rate risk are severely misspecified but also suggest that different model specifications have significant impact on term structure dynamics and prices of interest rate derivative securities.