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Title:

Renormalization group theory for fermions and order parameter fluctuations in interacting Fermi systems

Description:

In this thesis, we perform a comprehensive renormalization group analysis of two- and three-dimensional Fermi systems at low and zero temperature. We examine systems with spontaneous symmetry-breaking and quantum critical behavior by deriving and solving flow equations within the functional renormalization group framework. We extend the Hertz-Mi...

In this thesis, we perform a comprehensive renormalization group analysis of two- and three-dimensional Fermi systems at low and zero temperature. We examine systems with spontaneous symmetry-breaking and quantum critical behavior by deriving and solving flow equations within the functional renormalization group framework. We extend the Hertz-Millis theory of quantum phase transitions in itinerant fermion systems to phases with discrete and continuous symmetry-breaking, and to quantum critical points where the zero temperature theory is associated with a non-Gaussian fixed point. We compute the finite temperature phase boundary near the quantum critical point explicitly including non-Gaussian fluctuations. We then set up a coupled fermion-boson renormalization group theory that captures the mutual interplay of gapless fermions with massless order parameter fluctuations when approaching a quantum critical point. As a first application, we compute the complete set of quantum critical exponents at the semimetal-to-superfluid quantum phase transition of attractively interacting Dirac fermions in two dimensions. Both, the order parameter propagator and the fermion propagator become non-analytic functions of momenta destroying the Fermi liquid behavior. We finally compute the effects of quantum fluctuations in the superfluid ground state of an attractively interacting Fermi system, employing the attractive Hubbard model as a prototype. The flow equations capture the influence of longitudinal and Goldstone order parameter fluctuations on non-universal quantities such as the fermionic gap and the fermion-boson vertex, as well as the exact universal infrared asymptotics present in every fermionic superfluid. ; Comment: PhD thesis (Advisor: Walter Metzner), 125 pages; includes references to accompanying publications Minimize

Year of Publication:

2011-09-08

Document Type:

text

Subjects:

Condensed Matter - Strongly Correlated Electrons ; Condensed Matter - Statistical Mechanics ; High Energy Physics - Theory

Condensed Matter - Strongly Correlated Electrons ; Condensed Matter - Statistical Mechanics ; High Energy Physics - Theory Minimize

DDC:

539 Modern physics *(computed)*

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Title:

Dynamic criticality far-from-equilibrium: one-loop flow of Burgers-Kardar-Parisi-Zhang systems with broken Galilean invariance

Description:

We study dissipative soft matter systems subject to random driving with long-range temporal correlations the latter purposefully breaking the Galilean invariance of Burgers-Kardar-Parisi-Zhang fluids and interfaces. We compute the phase diagram and critical exponents of the KPZ equation with $1/f$-noise in spatial dimensions $1\leq d < 4$ using ...

We study dissipative soft matter systems subject to random driving with long-range temporal correlations the latter purposefully breaking the Galilean invariance of Burgers-Kardar-Parisi-Zhang fluids and interfaces. We compute the phase diagram and critical exponents of the KPZ equation with $1/f$-noise in spatial dimensions $1\leq d < 4$ using the dynamic renormalization group with a frequency cutoff technique in a one-loop truncation. We find the rough phase at high noise levels to violate fluctuation-dissipation relations, to exhibit hyperthermal statistics and self-organized criticality, and thereby to constitute a universality class truly far removed from thermal equilibrium. The fixed point associated with the roughening transition fulfills an emergent thermal-like fluctuation-dissipation relation. We point out potential connections to nonlinear hydrodynamics with a reduced set of conservation laws and noisy quantum liquids. ; Comment: 26 pages, 11 figures, 1 table, 40 references Minimize

Year of Publication:

2014-08-06

Document Type:

text

Subjects:

Condensed Matter - Statistical Mechanics ; Condensed Matter - Quantum Gases ; High Energy Physics - Theory

Condensed Matter - Statistical Mechanics ; Condensed Matter - Quantum Gases ; High Energy Physics - Theory Minimize

DDC:

612 Human physiology *(computed)*

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Title:

Renormalization group theory for fermions and order parameter fluctuations in interacting Fermi systems

Description:

The physics of interacting Fermi systems is extremely sensitive to the energy scale. Of particular interest is the low energy regime where correlation induced collective behavior emerges. The theory of interacting Fermi systems is confronted with the occurrence of very different phenomena along a continuum of scales calling for methods capable o...

The physics of interacting Fermi systems is extremely sensitive to the energy scale. Of particular interest is the low energy regime where correlation induced collective behavior emerges. The theory of interacting Fermi systems is confronted with the occurrence of very different phenomena along a continuum of scales calling for methods capable of computing physical observables as a function of energy scale. In this thesis, we perform a comprehensive renormalization group analysis of two and three-dimensional Fermi systems at low and zero temperature. We examine systems with spontaneous symmetry-breaking and quantum critical behavior by deriving and solving flow equations within the functional renormalization group framework. We extend the Hertz-Millis theory of quantumphase transitions in itinerant fermion systems to phases with discrete and continuous symmetry-breaking, and to quantum critical points where the zero temperature theory is associated with a non-Gaussian fixed point. The order parameter is implemented by a bosonic Hubbard-Stratonovich field, which –for continuous symmetry-breaking– splits into two components corresponding to longitudinal and transversal Goldstone fluctuations. We compute the finite temperature phase boundary near the quantum critical point explicitly including non-Gaussian fluctuations. We then set up a coupled fermion-boson renormalization group theory that captures the mutual interplay of gapless fermions with massless order parameter fluctuations when approaching a quantum critical point. As a first application, we compute the complete set of quantum critical exponents at the semimetal-to-superfluid quantum phase transition of attractively interacting Dirac fermions in two dimensions. Both, the order parameter propagator and the fermion propagator become nonanalytic functions of momenta destroying the Fermi liquid behavior. We finally compute the effects of quantum fluctuations in the superfluid ground state of an attractively interacting Fermi system, employing the attractive Hubbard model as a prototype. The flow equations capture the influence of longitudinal and Goldstone order parameter fluctuations on non-universal quantities such as the fermionic gap and the fermion-boson vertex, as well as the exact universal infrared asymptotics present in every fermionic superfluid. ; Die vorliegende Dissertation entwickelt Renormierungsgruppenstrategien zur Berechnung makroskopischer Eigenschaften von wechselwirkenden Fermi-Systemen. Besonders das Verhalten bei niederen Energien ist interessant, da hier wechselwirkungsinduzierte, kollektive Phänomene auftreten. Durch Herleitung und Lösung von Renormierungsgruppengleichungen analysieren wir in dieser Arbeit den Einfluss von Ordnungsparameterfluktuationen auf thermodynamische Observable und Korrelationsfunktionen in Fermi-Systemen mit spontaner Symmetriebrechung und quantenkritischem Verhalten. Minimize

Publisher:

Universität Stuttgart ; Wissenschaftliche Einrichtungen in Verbindung mit der Universität Stuttgart. Max-Planck-Institut für Festkörperforschung

Year of Publication:

2009

Document Type:

Thesis.Doctoral

Language:

eng

Subjects:

Statistische Physik ; Theoretische Physik ; Renormierungsgruppe ; Elektron ; Quantenkritische Phänomene ; Korrelierte Elektronen ; Quantum critical phenoemena ; correlated electrons ; Physics

Statistische Physik ; Theoretische Physik ; Renormierungsgruppe ; Elektron ; Quantenkritische Phänomene ; Korrelierte Elektronen ; Quantum critical phenoemena ; correlated electrons ; Physics Minimize

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Rights:

http://elib.uni-stuttgart.de/opus/doku/lic_mit_pod.php

http://elib.uni-stuttgart.de/opus/doku/lic_mit_pod.php Minimize

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Title:

Eine Christliche Leichpredigt/ Bey der Trawrigen Begrebnüß/ Weiland der . Frawen/ Gerdraut Glaßwellin/ deß . Stephan Grossen Seligen/ Bürgern zum Kirchhagen hinderlassenen Wittiwen/ welche den 11. Novembris . eingeschlaffen/ und den 15. Novembris zu Kirchhagen Ehrlich zur Erden bestattet worden/ Anno 1606

Publisher:

Wessel

Year of Publication:

1608

Source:

Strack, Philipp: Eine Christliche Leichpredigt/ Bey der Trawrigen Begrebnüß/ Weiland der . Frawen/ Gerdraut Glaßwellin/ deß . Stephan Grossen Seligen/ Bürgern zum Kirchhagen hinderlassenen Wittiwen/ welche den 11. Novembris . eingeschlaffen/ und den 15. Novembris zu Kirchhagen Ehrlich zur Erden bestattet worden/ Anno 1606. Cassel 1608

Strack, Philipp: Eine Christliche Leichpredigt/ Bey der Trawrigen Begrebnüß/ Weiland der . Frawen/ Gerdraut Glaßwellin/ deß . Stephan Grossen Seligen/ Bürgern zum Kirchhagen hinderlassenen Wittiwen/ welche den 11. Novembris . eingeschlaffen/ und den 15. Novembris zu Kirchhagen Ehrlich zur Erden bestattet worden/ Anno 1606. Cassel 1608 Minimize

Document Type:

Monograph ; Text

Subjects:

VD17-nova

VD17-nova Minimize

Rights:

Open Access

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Title:

Continuois Time Contests

Description:

This paper introduces a contest model in which each player decides when to stop a privately observed Brownian motion with drift and incurs costs depending on his stopping time. The player who stops his process at the highest value wins a prize. Applications of the model include procurement contests and competitions for grants. We prove existence...

This paper introduces a contest model in which each player decides when to stop a privately observed Brownian motion with drift and incurs costs depending on his stopping time. The player who stops his process at the highest value wins a prize. Applications of the model include procurement contests and competitions for grants. We prove existence and uniqueness of the Nash equilibrium outcome, even if players have to choose bounded stopping times. We derive the equilibrium distribution in closed form. If the noise vanishes, the equilibrium outcome converges to - and thus selects - the symmetric equilibrium outcome of an all-pay auction. For two players and constant costs, each player's profits increase if costs for both players increase, variance increases, or drift decreases. Intuitively, patience becomes a more important factor for contest success, which reduces informational rents. Minimize

Publisher:

Sonderforschungsbereich/Transregio 15 Governance and the Efficiency of Economic Systems München

Year of Publication:

2012

Document Type:

doc-type:workingPaper

Language:

eng

Subjects:

ddc:330 ; Contests ; all-pay contests ; silent timing games ; Entscheidung bei Risiko ; Glücksspiel ; Nichtkooperatives Spiel ; Zeitökonomie ; Theorie

ddc:330 ; Contests ; all-pay contests ; silent timing games ; Entscheidung bei Risiko ; Glücksspiel ; Nichtkooperatives Spiel ; Zeitökonomie ; Theorie Minimize

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Rights:

http://www.econstor.eu/dspace/Nutzungsbedingungen

http://www.econstor.eu/dspace/Nutzungsbedingungen Minimize

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SFB/TR 15 Discussion Paper 376

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Title:

Gambling in Contests

Description:

This paper presents a strategic model of risk-taking behavior in contests. Formally, we analyze an n-player winner-take-all contest in which each player decides when to stop a privately observed Brownian Motion with drift. A player whose process reaches zero has to stop. The player with the highest stopping point wins. Contrary to the explicit c...

This paper presents a strategic model of risk-taking behavior in contests. Formally, we analyze an n-player winner-take-all contest in which each player decides when to stop a privately observed Brownian Motion with drift. A player whose process reaches zero has to stop. The player with the highest stopping point wins. Contrary to the explicit cost for a higher stopping time in a war of attrition, here, higher stopping times are riskier, because players can go bankrupt. We derive a closed-form solution of the unique Nash equilibrium outcome of the game. In equilibrium, the trade-off between risk and reward causes a non-monotonicity: highest expected losses occur if the process decreases only slightly in expectation. Minimize

Publisher:

Sonderforschungsbereich/Transregio 15 Governance and the Efficiency of Economic Systems München

Year of Publication:

2012

Document Type:

doc-type:workingPaper

Language:

eng

Subjects:

C72 ; C73 ; D81 ; ddc:330 ; Discontinuous games ; Contests ; Relative performance pay ; Risktaking behavior ; Entscheidung bei Risiko ; Glücksspiel ; Nichtkooperatives Spiel ; Test

C72 ; C73 ; D81 ; ddc:330 ; Discontinuous games ; Contests ; Relative performance pay ; Risktaking behavior ; Entscheidung bei Risiko ; Glücksspiel ; Nichtkooperatives Spiel ; Test Minimize

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Rights:

http://www.econstor.eu/dspace/Nutzungsbedingungen

http://www.econstor.eu/dspace/Nutzungsbedingungen Minimize

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SFB/TR 15 Discussion Paper 375

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Title:

Too proud to stop: Regret in dynamic decisions

Description:

Many economic situations involve the timing of irreversible decisions. E.g. People decide when to sell a stock or stop searching for a better price. We analyze the behavior of a decision maker who evaluates his choice relative to the ex-post optimal choice in an optimal stopping task. We derive the optimal strategy under such regret preferences,...

Many economic situations involve the timing of irreversible decisions. E.g. People decide when to sell a stock or stop searching for a better price. We analyze the behavior of a decision maker who evaluates his choice relative to the ex-post optimal choice in an optimal stopping task. We derive the optimal strategy under such regret preferences, and show how it is different from that of an expected utility maximizer. We also show that if the decision maker never commits mistakes the behavior resulting from this strategy is observationally equivalent to that of an expected utility maximizer. We then test our theoretical predictions in the laboratory. The results from a structural discrete choice model we fit to our data provide strong evidence that many people's stopping behavior is largely determined by the anticipation of and aversion to regret. Minimize

Publisher:

Deutsches Institut für Wirtschaftsforschung (DIW) Berlin

Year of Publication:

2014

Document Type:

doc-type:workingPaper

Language:

eng

Subjects:

D03 ; C91 ; ddc:330 ; Optimal stopping ; Dynamic behavior ; Regret

D03 ; C91 ; ddc:330 ; Optimal stopping ; Dynamic behavior ; Regret Minimize

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Rights:

http://www.econstor.eu/dspace/Nutzungsbedingungen

http://www.econstor.eu/dspace/Nutzungsbedingungen Minimize

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Discussion Papers, DIW Berlin 1401

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Title:

Soft quantum vibrations of PT-symmetric nonlinear ion chain

Description:

We theoretically study the quantum dynamics of transverse vibrations of a one-dimensional chain of trapped ions in harmonic potentials interacting via a Reggeon-type cubic nonlinearity that is nonunitary but preserves PT symmetry. We propose the notion of quantum fragility for the dissipative structural phase transition that spontaneously breaks...

We theoretically study the quantum dynamics of transverse vibrations of a one-dimensional chain of trapped ions in harmonic potentials interacting via a Reggeon-type cubic nonlinearity that is nonunitary but preserves PT symmetry. We propose the notion of quantum fragility for the dissipative structural phase transition that spontaneously breaks the PT symmetry. In the quantum fragile regime, the nonlinearity dominates the response to mechanical perturbations and the chain supports neither the ordinary quantum phonons of a Luttinger liquid, nor the supersonic solitons that arise in classical fragile critical points in the absence of fluctuations. Quantum fluctuations, approximately captured within a one-loop renormalization group, give rise to mechanical excitations with a strongly momentum-dependent phonon velocity and dissipative spectral behavior. Observable signatures of the quantum fragile chain in trapped ion systems are discussed. ; Comment: 7 pages, 3 figures, as published Minimize

Year of Publication:

2013-02-18

Document Type:

text

Subjects:

Condensed Matter - Quantum Gases ; Condensed Matter - Statistical Mechanics ; High Energy Physics - Theory ; Quantum Physics

Condensed Matter - Quantum Gases ; Condensed Matter - Statistical Mechanics ; High Energy Physics - Theory ; Quantum Physics Minimize

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Title:

Dicke quantum spin glass of atoms and photons

Description:

Recent studies of strongly interacting atoms and photons in optical cavities have rekindled interest in the Dicke model of atomic qubits coupled to discrete photon cavity modes. We study the multimode Dicke model with variable atom-photon couplings. We argue that a quantum spin glass phase can appear, with a random linear combination of the cavi...

Recent studies of strongly interacting atoms and photons in optical cavities have rekindled interest in the Dicke model of atomic qubits coupled to discrete photon cavity modes. We study the multimode Dicke model with variable atom-photon couplings. We argue that a quantum spin glass phase can appear, with a random linear combination of the cavity modes superradiant. We compute atomic and photon spectral response functions across this quantum phase transition, both of which should be accessible in experiment. ; Comment: 4 pages, 3 figures, v2: described quantum optics set-up in more detail; extended discussion on photon correlation functions and experimental signatures; added references Minimize

Year of Publication:

2011-09-09

Document Type:

text

Subjects:

Condensed Matter - Quantum Gases ; Condensed Matter - Disordered Systems and Neural Networks ; Quantum Physics

Condensed Matter - Quantum Gases ; Condensed Matter - Disordered Systems and Neural Networks ; Quantum Physics Minimize

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Title:

Inverse Optimal Stopping

Description:

Let $X$ be a one-dimensional diffusion and $g$ a payoff function depending on time and the value of $X$. The paper analyzes the inverse optimal stopping problem of finding a time-dependent function $\pi:[0,T]\to\mathbb{R}$ such that a given stopping time $\tau^{\star}$ is a solution of the stopping problem \[ \{\tau^{\star}\}=\arg\sup_{\tau\in[0...

Let $X$ be a one-dimensional diffusion and $g$ a payoff function depending on time and the value of $X$. The paper analyzes the inverse optimal stopping problem of finding a time-dependent function $\pi:[0,T]\to\mathbb{R}$ such that a given stopping time $\tau^{\star}$ is a solution of the stopping problem \[ \{\tau^{\star}\}=\arg\sup_{\tau\in[0,T]}\mathbb{E}\left[g(\tau,X_{\tau})+\pi(\tau)\right]\,. \] Under regularity and monotonicity conditions, there exists a solution $\pi$ if and only if $\tau^{\star}$ is the first time $X$ exceeds a time-dependent cut-off $b$, i.e. $\tau^{\star}=\inf\left\{ t\ge0\,|\, X_{t}\ge b(t)\right\} \,.$ We prove uniqueness of the solution $\pi$ and derive a closed form representation. The representation is based on the process $\tilde{X}$ which is a version of the original diffusion $X$ reflected at $b$, \[ \pi(t)=\mathbb{E}\left[\int_{t}^{T}(\partial_{t}+\mathcal{L}g)(s,\tilde{X}_{s})\mathrm{d}s\,|\,\tilde{X}_{t}=b(t)\right]\,. \] The results lead to a new integral equation characterizing the stopping boundary $b$ of the stopping problem $\sup_{\tau\in\mathcal{T}}\mathbb{E}\left[g(\tau,X_{\tau})\right]$. Minimize

Year of Publication:

2014-06-01

Document Type:

text

Subjects:

Mathematics - Optimization and Control ; Mathematics - Probability ; Quantitative Finance - Economics

Mathematics - Optimization and Control ; Mathematics - Probability ; Quantitative Finance - Economics Minimize

DDC:

512 Algebra *(computed)*

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