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

Determinants of German Foreign Direct Investment in Latin American and Asian Emerging Markets in the 1990s

Many empirical studies in the area of foreign direct investment (FDI) exclusively focus on flows between industrialized countries. This article makes a contribution to the still relatively sparse literature on FDI in emerging markets by estimating determinants of German FDI flows to Latin America and Asia during the past decade. Using data contained in a newly available Bundesbank microdatabase, an FDI flow variable, constructed from year-to-year differences in FDI stocks adjusted for certain otherwise distorting factors, is empirically tested with respect to several exogenous variables previously found to be significant in the literature. These include so-called non-traditional factors such as country risk and agglomeration effects which are widely regarded as influential for FDI in emerging market economies. This study therefore focuses on estimating the effects of various risk measures and finds that country risk, and partially political risk, is indeed detrimental to investments of German enterprises. Moreover, German FDI in Latin America are found to have been market-seeking while those in emerging Asia tended to exploit low factor costs. Methodically, this paper uses the SUR estimation technique which allows for the contemporaneous correlation of disturbances as well as first-order autocorrelation of the time series disturbances and cross-sectional heteroskedasticity. In arriving at a parsimonious regression for each region, an Extreme Bounds Analysis (Leamer, 1983 & 1985) is performed to select individual variables robust to the inclusion of other explanatory variables. Making empirical use of German firm-level data, additional estimations are performed for direct investment of the manufacturing sector and three of its sub-sectors. Regarding the latter, the hypothesis that capital-intensive industries react particularly strongly to the changes in the regulatory environment of the host country is confirmed by the data. -- Viele empirische Studien im Bereich der ausländischen Direktinvestitionen (?foreign direct investment? ? ?FDI?) beziehen sich ausschließlich auf Investitionsströme zwischen Industrieländern. Dieses Arbeitspapier trägt zu der noch vergleichsweise spärlichen Literatur zu Direktinvestitionen in Schwellenländern bei. Es schätzt die Determinanten deutscher FDIStröme in ausgewählten ?Emerging Markets? während der letzten Dekade. Mit Hilfe von Daten, die in einer seit kurzem verfügbaren Mikrodatenbank der Bundesbank enthalten sind, wird eine Stromgröße, die sich aus den Bestandsveränderungen der Direktinvestitionsbestände errechnet und die um verzerrende Einflüsse bereinigt wird, empirisch hinsichtlich verschiedener exogener, in der Literatur als signifikant befundener Variablen überprüft. Diese schließen sogenannte nicht-traditionelle Faktoren wie Länderrisiko und Agglomerationseffekte ein, die allgemein als einflussreich für Direktinvestitionen in Schwellenländern erachtet werden. Die vorliegende Studie konzentriert sich demnach auf die Schätzung der Bedeutung verschiedener Risikomaße und findet, dass das Länderrisiko und teilweise auch das politische Risiko den Investitionen deutscher Unternehmen abträglich sind. Außerdem wird gezeigt, dass deutsche Direktinvestitionen in Lateinamerika eher markterschließend waren, während jene in den Schwellenländern Asiens stärker die Nutzung niedriger Faktorkosten zum Ziel hatten. Methodisch wird die SUR Schätzmethode angewandt, die eine Berücksichtigung gruppenweiser Korrelation der Störgrößen, eines autoregressiven Prozesses erster Ordnung und Heteroskedastizität ermöglicht. Um ein sparsames Modell schätzen zu können, wird eine ?Extreme Bounds?-Analyse nach Leamer (1983 & 1985) durchgeführt, welche die Auswahl von solchen Variablen bezweckt, deren Einfluss gegen die Einbeziehung anderer exogener Variablen robust ist. Zudem werden Einzeldaten deutscher Firmen genutzt, um weitere Schätzungen der Direktinvestitionen des Verarbeitenden Gewerbes und dreier Untersektoren durchzuführen. Bezüglich Letzterer kann die Hypothese, dass kapitalintensive Sektoren besonders stark auf Änderungen im regulatorischen Umfeld der Empfängerländer reagieren, mit Hilfe der Daten bestätigt werden.foreign direct investment,emerging markets,country risk,panel data analysis

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

Why do organizational populations die? : evidence from the Belgian motorcycle industry, 1900-1993

Extinctions represent a potential outcome of the evolutionary processes of organizational populations. Nevertheless, scant effort, if none, has been dedicated to investigate this issue. This paper proposes three alternative hypotheses that may account for extinction events. They are drawn from very different literatures: economic geography, economic sociology, and evolutionary biology/paleontology. In particular, two of them rely on exogenous determinants, while one is focused on an endogenous reasoning. The theory presented is tested analyzing the entries of motorcycle producers in Belgium, a population that ceased to exist in 1981. The findings of this research provide evidence to support the internal causation of the event. The implications stemming from the present work are related to the literatures of population ecology and industrial economics.