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Academic Commons Search Resultsen-usHolographic Jet Quenching
http://academiccommons.columbia.edu/catalog/ac:178237
Ficnar, Andrejhttp://dx.doi.org/10.7916/D8M04417Wed, 08 Oct 2014 00:00:00 +0000In this dissertation we study the phenomenon of jet quenching in quark-gluon plasma using the AdS/CFT correspondence. We start with a weakly coupled, perturbative QCD approach to energy loss, and present a Monte Carlo code for computation of the DGLV radiative energy loss of quarks and gluons at an arbitrary order in opacity. We use the code to compute the radiated gluon distribution up to n=9 order in opacity, and compare it to the thin plasma (n=1) and the multiple soft scattering (n=\infty) approximations. We furthermore show that the gluon distribution at finite opacity depends in detail on the screening mass and the mean free path. In the next part, we turn to the studies of how heavy quarks, represented as "trailing strings" in AdS/CFT, lose energy in a strongly coupled plasma. We study how the heavy quark energy loss gets modified in a "bottom-up" non-conformal holographic model, constructed to reproduce some properties of QCD at finite temperature and constrained by fitting the lattice gauge theory results. The energy loss of heavy quarks is found to be strongly sensitive to the medium properties. We use this model to compute the nuclear modification factor R_AA of charm and bottom quarks in an expanding plasma with Glauber initial conditions, and comment on the range of validity of the model. The central part of this thesis is the energy loss of light quarks in a strongly coupled plasma. Using the standard model of "falling strings", we present an analytic derivation of the stopping distance of light quarks, previously available only through numerical simulations, and also apply it to the case of Gauss-Bonnet higher derivative gravity. We then present a general formula for computing the instantaneous energy loss in non-stationary string configurations. Application of this formula to the case of falling strings reveals interesting phenomenology, including a modified Bragg-like peak at late times and an approximately linear path dependence. Based on these results, we develop a phenomenological model of light quark energy loss and use it compute the nuclear modification factor R_AA of light quarks in an expanding plasma. Comparison with the LHC pion suppression data shows that, although R_AA has the right qualitative structure, the overall magnitude is too low, indicating that the predicted jet quenching is too strong. In the last part of the thesis we consider a novel idea of introducing finite momentum at endpoints of classical (bosonic and supersymmetric) strings, and the phenomenological consequences of this proposal on the energy loss of light quarks. We show that in a general curved background, finite momentum endpoints must propagate along null geodesics and that the distance they travel in an AdS5-Schwarzschild background is greater than in the previous treatments of falling strings. We also argue that this leads to a more realistic description of energetic quarks, allowing for an unambiguous way of distinguishing between the energy in the dual hard probe and the energy in the color fields surrounding it. This proposal also naturally allows for a clear and simple definition of the instantaneous energy loss. Using this definition and the "shooting string" initial conditions, we develope a new formula for light quark energy loss. Finally, we apply this formula to compute the nuclear modification factor R_AA of light hadrons at RHIC and LHC, which, after the inclusion of the Gauss-Bonnet quadratic curvature corrections to the AdS5 geometry, shows a reasonably good agreement with the recent data.Physics, Theoretical physics, Nuclear physicsaf2440PhysicsDissertationsNegative Modes in Vacuum Decay
http://academiccommons.columbia.edu/catalog/ac:176867
Lee, Hak Joonhttp://dx.doi.org/10.7916/D84X55Z3Mon, 07 Jul 2014 00:00:00 +0000A vacuum, a classically stable state, can decay to another vacuum by virtue of quantum tunneling. Although vacuum decay is an interesting topic itself in field theory, when it combines with gravity, it has wider applications and plays an essential role to understand the very early universe. The semi-classical solution of vacuum decay is well-described by the WKB approximation both in flat space and in curved space. Meanwhile, if we consider the configuration space of fields, we encounter many kinds of problems related with gravitational fields since the mode spectrum in curved space turns out to have an infinite number of negative modes in a de Sitter background. Despite of infinitely many negative modes, the regime in the weak gravity limit can be smoothly connected to flat space. To understand this, I discuss the nature of vacuum decay and various topics about negative modes in this thesis.Theoretical physics, Particle physicshl2406PhysicsDissertationsNovel Quantum Monte Carlo Approaches for Quantum Liquids
http://academiccommons.columbia.edu/catalog/ac:188891
Rubenstein, Brenda M.http://dx.doi.org/10.7916/D8N58KRKTue, 20 Aug 2013 00:00:00 +0000Quantum Monte Carlo methods are a powerful suite of techniques for solving the quantum many-body problem. By using random numbers to stochastically sample quantum properties, QMC methods are capable of studying low-temperature quantum systems well beyond the reach of conventional deterministic techniques. QMC techniques have likewise been indispensible tools for augmenting our current knowledge of superfluidity and superconductivity. In this thesis, I present two new quantum Monte Carlo techniques, the Monte Carlo Power Method and Bose-Fermi Auxiliary-Field Quantum Monte Carlo, and apply previously developed Path Integral Monte Carlo methods to explore two new phases of quantum hard spheres and hydrogen. I lay the foundation for a subsequent description of my research by first reviewing the physics of quantum liquids in Chapter One and the mathematics behind Quantum Monte Carlo algorithms in Chapter Two. I then discuss the Monte Carlo Power Method, a stochastic way of computing the first several extremal eigenvalues of a matrix too memory-intensive to be stored and therefore diagonalized. As an illustration of the technique, I demonstrate how it can be used to determine the second eigenvalues of the transition matrices of several popular Monte Carlo algorithms. This information may be used to quantify how rapidly a Monte Carlo algorithm is converging to the equilibrium probability distribution it is sampling. I next present the Bose-Fermi Auxiliary-Field Quantum Monte Carlo algorithm. This algorithm generalizes the well-known Auxiliary-Field Quantum Monte Carlo algorithm for fermions to bosons and Bose-Fermi mixtures. Despite some shortcomings, the Bose-Fermi Auxiliary-Field Quantum Monte Carlo algorithm represents the first exact technique capable of studying Bose-Fermi mixtures of any size in any dimension. In Chapter Six, I describe a new Constant Stress Path Integral Monte Carlo algorithm for the study of quantum mechanical systems under high pressures. While the eventual hope is to apply this algorithm to the exploration of yet unidentified high-pressure, low-temperature phases of hydrogen, I employ this algorithm to determine whether or not quantum hard spheres can form a low-temperature bcc solid if exchange is not taken into account. In the final chapter of this thesis, I use Path Integral Monte Carlo once again to explore whether glassy para-hydrogen exhibits superfluidity. Physicists have long searched for ways to coax hydrogen into becoming a superfluid. I present evidence that, while glassy hydrogen does not crystallize at the temperatures at which hydrogen might become a superfluid, it nevertheless does not exhibit superfluidity. This is because the average binding energy per p-H2 molecule poses a severe barrier to exchange regardless of whether the system is crystalline. All in all, this work extends the reach of Quantum Monte Carlo methods to new systems and brings the power of existing methods to bear on new problems.Theoretical physicsbr2197Chemistry, Chemical PhysicsDissertationsUniversality in selection with local perturbations in the Saffman-Taylor problem
http://academiccommons.columbia.edu/catalog/ac:162398
Shaw, Bruce E.http://hdl.handle.net/10022/AC:P:20764Mon, 17 Jun 2013 00:00:00 +0000An analytic theory using WKBJ methods for selection with local perturbations in the SaffmanTaylor [Proc. R. Soc. London, Ser. A 245, 312 (1958)] problem is presented. I obtain qualitative agreement with previously published phenomenology, including symmetric narrowed fingers for local reductions in the surface-tension parameter, narrowed asymmetric fingers for local increases, and scaling of the tip curvature and asymmetry with the square root of the surface-tension parameter. The source of the universality in the perturbed problem is discussed, giving some explanation of why the experimental perturbations can be modeled by locally varying surface tension. Very good quantitative agreement between theory and a numerical simulation of the same perturbation is shown, with no adjustable parameters to fit. Finally, I outline experiments to test new behavior predicted by the theory; a quantitative prediction observable experimentally is given.Theoretical physics, Mechanicsbes11Lamont-Doherty Earth ObservatoryArticlesIntrinsic properties of a Burridge-Knopoff model of an earthquake fault
http://academiccommons.columbia.edu/catalog/ac:162401
Carlson, Jean M.; Langer, James S.; Shaw, Bruce E.; Tang, Chaohttp://hdl.handle.net/10022/AC:P:20765Mon, 17 Jun 2013 00:00:00 +0000We present a detailed numerical study of certain fundamental aspects of a one-dimensional homogeneous, deterministic Burridge-Knopoff model. The model is described by a massive wave equation, in which the key nonlinearity is associated with the stick-slip velocity-weakening friction force at the interface between tectonic plates. In this paper, we present results for the statistical distribution of slipping events in the limit of a very long fault and infinitesimally slow driving rates. Typically, we find that the magnitude distribution of smaller events is consistent with the Gutenberg-Richter law, while the larger events occur in excess of this distribution. The crossover from smaller to larger events is identified with a correlation length describing the transition from localized to delocalized events. We also find that there is a sharp upper cutoff describing the maximum large event. We identify how the correlation length and this upper cutoff scale with the parameters in the model. We find that both are independent of system size, while both do depend on the spatial discretization. In addition to the magnitude distribution, we present a series of measurements of other seismologically relevant quantities, including the event duration, the size of the rupture zone, and the energy release, and discuss the relationship between our measurements and the corresponding empirical laws in seismology.Theoretical physics, Plate tectonicsbes11Lamont-Doherty Earth ObservatoryArticlesFinger narrowing under local perturbations in the Saffman-Taylor problem
http://academiccommons.columbia.edu/catalog/ac:162376
Zocchi, Giovanni; Shaw, Bruce E.; Libchaber, Albert; Kadanoff, Leo P.http://hdl.handle.net/10022/AC:P:20749Fri, 14 Jun 2013 00:00:00 +0000We present an experimental study and a numerical simulation of the effect of time-independent, localized perturbations applied to the interface in the Saffman-Taylor fingering problem. When the perturbation is applied at a specific spot near the tip of the finger, the selection of the steady-state shape is drastically changed. In particular, one can obtain fingers with a width well below λ=1/2. A perturbation applied far away from the tip has no effect. We observe the same behavior in the simulation and in the experiment.Theoretical physics, Mechanicsbes11Lamont-Doherty Earth ObservatoryArticlesThe Effective Field Theory Approach to Fluid Dynamics
http://academiccommons.columbia.edu/catalog/ac:161458
Endlich, Solomonhttp://hdl.handle.net/10022/AC:P:20419Thu, 23 May 2013 00:00:00 +0000In this thesis we initiate a systematic study of fluid dynamics using the effective field theory (EFT) program. We consider the canonical quantization of an ordinary fluid in an attempt to discover if there is some kind of quantum mechanical inconsistency with ordinary fluids at zero temperature. The system exhibits a number of peculiarities associated with the vortex degrees of freedom. We also study the dynamics of a nearly incompressible fluid via (classical) effective field theory. In the kinematical regime corresponding to near incompressibility (small fluid velocities and accelerations), compressional modes are, by definition, difficult to excite, and can be dealt with perturbatively. We systematically outline the corresponding perturbative expansion, which can be thought of as an expansion in the ratio of fluid velocity and speed of sound. This perturbation theory allows us to compute many interesting quantities associated with sound-flow interactions. Additionally, we also improve on the so-called vortex filament model, by providing a local field theory describing the dynamics of vortex-line systems and their interaction with sound, to all orders in perturbation theory. Next, we develop a cosmological model where primordial inflation is driven by a 'solid'. The low energy EFT describing such a system is just a less symmetric version of the action of a fluid---it lacks the volume preserving diffeomorphism. The symmetry breaking pattern of this system differs drastically from that of standard inflationary models: time translations are unbroken. This prevents our model from fitting into the standard effective field theory description of adiabatic perturbations, with crucial consequences for the dynamics of cosmological perturbations. And finally, we introduce dissipative effects in the effective field theory of hydrodynamics. We do this in a model-independent fashion by coupling the long-distance degrees of freedom explicitly kept in the effective field theory to a generic sector that "lives in the fluid'', which corresponds physically to the microscopic constituents of the fluid. At linear order in perturbations, the symmetries, the derivative expansion, and the assumption that this microscopic sector is thermalized, allow us to characterize the leading dissipative effects at low frequencies via three parameters only, which correspond to bulk viscosity, shear viscosity, and---in the presence of a conserved charge---heat conduction. Using our methods we re-derive the Kubo relations for these transport coefficients.Theoretical physics, Physics, Condensed matter physicssge2104PhysicsDissertationsPrecision Lattice Calculation of Kaon Decays with Möbius Domain Wall Fermions
http://academiccommons.columbia.edu/catalog/ac:161136
Yin, Hantaohttp://hdl.handle.net/10022/AC:P:20325Tue, 14 May 2013 00:00:00 +0000We report our recent development in algorithms and progress in measurements in lattice QCD. The algorithmic development includes the forecasted force gradient integrator, and further theoretical development and implementation of the Möbius domain wall fermions. These new technologies make it practical to simulate large 48^3*96 and 64^3*128 lattice ensembles with (5.5fm)^3 boxes and 140MeV pion. The calculation was performed using the Möbius domain wall fermions and the Iwasaki gauge action. Simulated directly at physical quark masses, these ensembles are of great value for our ongoing and future lattice measurement projects. With the help of measurement techniques such as the eigCG algorithm and the all mode averaging method, we perform a direct, precise lattice calculation of the semileptonic kaon decay K→πlν using these newly generated high quality lattice ensembles. Our main result is the form factor f^+_{Kπ}(q^2) evaluated directly at zero momentum transfer q^2=0. Free of various systematic errors, this new result can be used to determine the CKM matrix element Vus to a very high precision when combined with experimental input. The calculation also provides results for various low energy strong interaction constants such as the pseudoscalar decay constants f_K and f_π, and the neutral kaon mixing matrix element B_K. These calculations are naturally performed by reusing the propagators calculated for the kaon semileptonic decay mentioned above. So they come with no or very low additional cost. The results allow us to also determine these important low energy constants on the lattice to unprecedented accuracy.Physics, Particle physics, Theoretical physicshy2242PhysicsDissertationsPrecision Lattice Calculation of Kaon Decays with Möbius Domain Wall Fermions
http://academiccommons.columbia.edu/catalog/ac:160818
Yin, Hantaohttp://hdl.handle.net/10022/AC:P:20151Wed, 01 May 2013 00:00:00 +0000We report our recent development in algorithms and progress in measurements in lattice QCD. The algorithmic development includes the forecasted force gradient integrator, and further theoretical development and implementation of the Möbius domain wall fermions. These new technologies make it practical to simulate large 48^3*96 and 64^3*128 lattice ensembles with (5.5fm)^3 boxes and 140MeV pion. The calculation was performed using the Möbius domain wall fermions and the Iwasaki gauge action. Simulated directly at physical quark masses, these ensembles are of great value for our ongoing and future lattice measurement projects.With the help of measurement techniques such as the eigCG algorithm and the all mode averaging method, we perform a direct, precise lattice calculation of the semileptonic kaon decay K→πlν using these newly generated high quality lattice ensembles. Our main result is the form factor f^+_{Kπ}(q^2) evaluated directly at zero momentum transfer q^2=0. Free of various systematic errors, this new result can be used to determine the CKM matrix element Vus to a very high precision when combined with experimental input. The calculation also provides results for various low energy strong interaction constants such as the pseudoscalar decay constants f_K and f_π, and the neutral kaon mixing matrix element B_K. These calculations are naturally performed by reusing the propagators calculated for the kaon semileptonic decay mentioned above. So they come with no or very low additional cost. The results allow us to also determine these important low energy constants on the lattice to unprecedented accuracy.Particle physics, Physics, Theoretical physicshy2242PhysicsDissertationsKaon to two pions decays from lattice QCD: ΔI=1/2 rule and CP violation
http://academiccommons.columbia.edu/catalog/ac:146416
Liu, Qihttp://hdl.handle.net/10022/AC:P:13068Mon, 30 Apr 2012 00:00:00 +0000We report a direct lattice calculation of the K to ππ decay matrix elements for both the ΔI = 1/2 and 3/2 amplitudes A0 and A2 on a 2+1 flavor, domain wall fermion, 163 × 32 × 16 lattice ensemble and a 243 × 64 × 16 lattice ensemble. This is a complete calculation in which all contractions for the required ten, four-quark operators are evaluated, including the disconnected graphs in which no quark line connects the initial kaon and final two-pion states. These lattice operators are nonperturbatively renormalized using the Rome-Southampton method and the quadratic divergences are studied and removed. This is an important but notoriously difficult calculation, requiring high statistics on a large volume. In this work we take a major step towards the computation of the physical K → ππ amplitudes by performing a complete calculation at unphysical kinematics with pions of mass 422MeV and 329MeV at rest in the kaon rest frame. With this simplification we are able to resolve Re(A0) from zero for the first time, with a 25% statistical error on the 163 lattice and 15% on the 243 lattice. The complex amplitude A2 is calculated with small statistical errors. We obtain the ΔI = 1/2 rule with an enhancement factor of 9.1(21) and 12.0(17) on these two ensembles. From the detailed analysis of the results we gain a deeper understanding of the origin of the ΔI = 1/2 rule. We also calculate the complex amplitude A0, a calculation central to understanding and testing the standard model of CP violation in the kaon system. The final result for the measure of direct CP violation, ε′, calculated at unphysical kinematics has an order of 100% statistical error, so this only serves as an order of magnitude check.Theoretical physicsql2142PhysicsDissertations