Publications with Fulltext
Permanent URI for this collectionhttps://hdl.handle.net/20.500.14288/6
Browse
46 results
Search Results
Publication Open Access Observation of two-photon interference using the zero-phonon-line emission of a single molecule(Institute of Physics (IOP) Publishing, 2006) Ehrl, M.; Hellerer, Th.; Brauchle, C.; Zumbusch, A.; Department of Physics; Department of Physics; Müstecaplıoğlu, Özgür Esat; Kiraz, Alper; Faculty Member; Faculty Member; College of Sciences; 1674; 22542We report the results of coincidence counting experiments at the output of a Michelson interferometer using the zero-phonon-line emission of a single molecule at 1.4 K. Under continuous wave excitation, we observe the absence of coincidence counts as an indication of two-photon interference. This corresponds to the observation of Hong-Ou-Mandel correlations.Publication Open Access Macroscopic loop formation in circular DNA denaturation(American Physical Society (APS), 2012) Bar, Amir; Mukamel, David; Department of Physics; Department of Physics; Kabakçıoğlu, Alkan; Faculty Member; College of Sciences; 49854The statistical mechanics of DNA denaturation under fixed linking number is qualitatively different from that of unconstrained DNA. Quantitatively different melting scenarios are reached from two alternative assumptions, namely, that the denatured loops are formed at the expense of (i) overtwist or (ii) supercoils. Recent work has shown that the supercoiling mechanism results in a picture similar to Bose-Einstein condensation where a macroscopic loop appears at T-c and grows steadily with temperature, while the nature of the denatured phase for the overtwisting case has not been studied. By extending an earlier result, we show here that a macroscopic loop appears in the overtwisting scenario as well. We calculate its size as a function of temperature and show that the fraction of the total sum of microscopic loops decreases above T-c, with a cusp at the critical point.Publication Open Access Differential realization of pseudo-Hermiticity: a quantum mechanical analog of Einstein's field equation(American Institute of Physics (AIP) Publishing, 2006) Department of Mathematics; Department of Mathematics; Mostafazadeh, Ali; Faculty Member; College of Sciences; 4231For a given pseudo-Hermitian Hamiltonian of the standard form: H=p(2)/2m+v(x), we reduce the problem of finding the most general (pseudo-)metric operator eta satisfying H(dagger)=eta H eta(-1) to the solution of a differential equation. If the configuration space is R, this is a Klein-Gordon equation with a nonconstant mass term. We obtain a general series solution of this equation that involves a pair of arbitrary functions. These characterize the arbitrariness in the choice of eta. We apply our general results to calculate eta for the PT-symmetric square well, an imaginary scattering potential, and a class of imaginary delta-function potentials. For the first two systems, our method reproduces the known results in a straightforward and extremely efficient manner. For all these systems we obtain the most general eta up to second-order terms in the coupling constants.Publication Open Access Buckling of stiff polymers: influence of thermal fluctuations(American Physical Society (APS), 2007) Emanuel, Marc; Mohrbach, Herve; Schiessel, Helmut; Kulic, Igor M.; Department of Mechanical Engineering; Department of Mechanical Engineering; Sayar, Mehmet; Faculty Member; College of Engineering; 109820The buckling of biopolymers is a frequently studied phenomenon The influence of thermal fluctuations on the buckling transition is, however, often ignored and not completely understood. A quantitative theory of the buckling of a wormlike chain based on a semiclassical approximation of the partition function is presented. The contribution of thermal fluctuations to the force-extension relation that allows one to go beyond the classical Euler buckling is derived in the linear and nonlinear regimes as well. It is shown that the thermal fluctuations in the nonlinear buckling regime increase the end-to-end distance of the semiflexible rod if it is confined to two dimensions as opposed to the three-dimensional case. The transition to a buckled state softens at finite temperature. We derive the scaling behavior of the transition shift with increasing ratio of contour length versus persistence length.Publication Open Access Pseudounitary operators and pseudounitary quantum dynamics(American Institute of Physics (AIP) Publishing, 2004) Department of Mathematics; Department of Mathematics; Mostafazadeh, Ali; Faculty Member; College of Sciences; 4231We consider pseudounitary quantum systems and discuss various properties of pseudounitary operators. In particular we prove a characterization theorem for block-diagonalizable pseudounitary operators with finite-dimensional diagonal blocks. Furthermore, we show that every pseudounitary matrix is the exponential of i=root-1 times a pseudo-Hermitian matrix, and determine the structure of the Lie groups consisting of pseudounitary matrices. In particular, we present a thorough treatment of 2x2 pseudounitary matrices and discuss an example of a quantum system with a 2x2 pseudounitary dynamical group. As other applications of our general results we give a proof of the spectral theorem for symplectic transformations of classical mechanics, demonstrate the coincidence of the symplectic group Sp(2n) with the real subgroup of a matrix group that is isomorphic to the pseudounitary group U(n,n), and elaborate on an approach to second quantization that makes use of the underlying pseudounitary dynamical groups.Publication Open Access Denaturation of circular DNA: supercoil mechanism 2011(American Physical Society (APS), 2011) Bar, Amir; Mukamel, David; Department of Physics; Department of Physics; Kabakçıoğlu, Alkan; Faculty Member; College of Sciences; 49854The denaturation transition which takes place in circular DNA is analyzed by extending the Poland-Scheraga (PS) model to include the winding degrees of freedom. We consider the case of a homopolymer whereby the winding number of the double-stranded helix, released by a loop denaturation, is absorbed by supercoils. We find that as in the case of linear DNA, the order of the transition is determined by the loop exponent c. However the first-order transition displayed by the PS model for c > 2 in linear DNA is replaced by a continuous transition with arbitrarily high order as c approaches 2, while the second-order transition found in the linear case in the regime 1 < c <= 2 disappears. In addition, our analysis reveals that melting under fixed linking number is a condensation transition, where the condensate is a macroscopic loop which appears above the critical temperature.Publication Open Access High-precision thermodynamic and critical properties from tensor renormalization-group flows(American Physical Society (APS), 2008) Hinczewski, Michael; Department of Physics; Department of Physics; Berker, Ahmet Nihat; Faculty Member; College of SciencesThe recently developed tensor renormalization-group (TRG) method provides a highly precise technique for deriving thermodynamic and critical properties of lattice Hamiltonians. The TRG is a local coarse-graining transformation, with the elements of the tensor at each lattice site playing the part of the interactions that undergo the renormalization-group flows. These tensor flows are directly related to the phase diagram structure of the infinite system, with each phase flowing to a distinct surface of fixed points. Fixed-point analysis and summation along the flows give the critical exponents, as well as thermodynamic functions along the entire temperature range. Thus, for the ferromagnetic triangular lattice Ising model, the free energy is calculated to better than 10(-5) along the entire temperature range. Unlike previous position-space renormalization-group methods, the truncation (of the tensor index range D) in this general method converges under straightforward and systematic improvements. Our best results are easily obtained with D=24, corresponding to 4624-dimensional renormalization-group flows.Publication Open Access Quantum mechanics of a photon(American Institute of Physics (AIP) Publishing, 2017) Department of Physics; Department of Mathematics; Department of Physics; Department of Mathematics; Babaei, Hassan; Mostafazadeh, Ali; Faculty Member; Graduate School of Sciences and Engineering; N/A; 4231A first-quantized free photon is a complex massless vector field A = (A(mu)) whose field strength satisfies Maxwell's equations in vacuum. We construct the Hilbert space H of the photon by endowing the vector space of the fields A in the temporal-Coulomb gauge with a positive-definite and relativistically invariant inner product. We give an explicit expression for this inner product, identify the Hamiltonian for the photon with the generator of time translations in H, determine the operators representing the momentum and the helicity of the photon, and introduce a chirality operator whose eigenfunctions correspond to fields having a definite sign of energy. We also construct a position operator for the photon whose components commute with each other and with the chirality and helicity operators. This allows for the construction of the localized states of the photon with a definite sign of energy and helicity. We derive an explicit formula for the latter and compute the corresponding electric and magnetic fields. These turn out to diverge not just at the point where the photon is localized but on a plane containing this point. We identify the axis normal to this plane with an associated symmetry axis and show that each choice of this axis specifies a particular position operator, a corresponding position basis, and a position representation of the quantum mechanics of a photon. In particular, we examine the position wave functions determined by such a position basis, elucidate their relationship with the Riemann-Silberstein and Landau-Peierls wave functions, and give an explicit formula for the probability density of the spatial localization of the photon.Publication Open Access Generalized unitarity relation for linear scattering systems in one dimension(Springer, 2019) Department of Physics; Department of Mathematics; Department of Physics; Department of Mathematics; Mostafazadeh, Ali; Faculty Member; College of Sciences; 4231We derive a generalized unitarity relation for an arbitrary linear scattering system that may violate unitarity, time-reversal invariance, PT - symmetry, and transmission reciprocity.Publication Open Access Global solvability and blow up for the convective Cahn-Hilliard equations with concave potentials(American Institute of Physics (AIP) Publishing, 2013) Eden, A.; Zelik, S. V.; Department of Mathematics; Department of Mathematics; Kalantarov, Varga; Faculty Member; college of sciences; 117655We study initial boundary value problems for the unstable convective Cahn-Hilliard (CH) equation, i.e., the Cahn Hilliard equation whose energy integral is not bounded below. It is well-known that without the convective term, the solutions of the unstable CH equation ?t u + ? 4xu + ?2x(|u|pu) = 0 may blow up in ?nite time for anyp > 0. In contrast to that, we show that the presence of the convective term u?xuin the Cahn-Hilliard equation prevents blow up at least for 0 < p <49. We alsoshow that the blowing up solutions still exist if p is large enough (p ? 2). The related equations like Kolmogorov-Sivashinsky-Spiegel equation, sixth order convective Cahn-Hilliard equation, are also considered.