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Permanent URI for this collectionhttps://hdl.handle.net/20.500.14288/6

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Department: search.filters.department.Department of PhysicsSubject: search.filters.subject.Mathematical physics

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Now showing 1 - 10 of 23
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    PublicationOpen 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; 22542
    We 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.
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    PublicationOpen 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; 49854
    The 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.
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    PublicationOpen 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; 49854
    The 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.
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    PublicationOpen 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 Sciences
    The 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.
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    PublicationOpen 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; 4231
    A 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.
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    PublicationOpen 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; 4231
    We derive a generalized unitarity relation for an arbitrary linear scattering system that may violate unitarity, time-reversal invariance, PT - symmetry, and transmission reciprocity.
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    PublicationOpen Access
    Interface-roughening phase diagram of the three-dimensional Ising model for all interaction anisotropies from hard-spin mean-field theory
    (American Physical Society (APS), 2011) Department of Physics; Department of Physics; Berker, Ahmet Nihat; Faculty Member; College of Sciences
    The roughening phase diagram of the d = 3 Ising model with uniaxially anisotropic interactions is calculated for the entire range of anisotropy, from decoupled planes to the isotropic model to the solid-on-solid model, using hard-spin mean-field theory. The phase diagram contains the line of ordering phase transitions and, at lower temperatures, the line of roughening phase transitions, where the interface between ordered domains roughens. Upon increasing the anisotropy, roughening transition temperatures settle after the isotropic case, whereas the ordering transition temperature increases to infinity. The calculation is repeated for the d = 2 Ising model for the full range of anisotropy, yielding no roughening transition.
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    PublicationOpen Access
    Quantum correlated heat engine with spin squeezing
    (American Physical Society (APS), 2014) Altıntaş, Ferdi; Department of Physics; Department of Physics; Hardal, Ali Ümit Cemal; Müstecaplıoğlu, Özgür Esat; Faculty Member; Graduate School of Sciences and Engineering; College of Sciences; N/A; 1674
    We propose a four-level quantum heat engine in an Otto cycle with a working substance of two spins subject to an external magnetic field and coupled to each other by a one-axis twisting spin squeezing nonlinear interaction. We calculate the positive work and the efficiency of the engine for different parameter regimes. In particular, we investigate the effects of quantum correlations at the end of the two isochoric processes of the Otto cycle, as measured by the entanglement of formation and quantum discord, on the work extraction and efficiency. The regimes where the quantum correlations could enhance the efficiency and work extraction are characterized.
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    PublicationOpen Access
    Strong violation of critical phenomena universality: Wang-Landau study of the two-dimensional Blume-Capel model under bond randomness
    (American Physical Society (APS), 2009) Malakis, A.; Hadjiagapiou, I. A.; Fytas, N. G.; Department of Physics; Department of Physics; Berker, Ahmet Nihat; Faculty Member; College of Sciences
    We study the pure and random-bond versions of the square lattice ferromagnetic Blume-Capel model, in both the first-order and second-order phase transition regimes of the pure model. Phase transition temperatures, thermal and magnetic critical exponents are determined for lattice sizes in the range L=20-100 via a sophisticated two-stage numerical strategy of entropic sampling in dominant energy subspaces, using mainly the Wang-Landau algorithm. The second-order phase transition, emerging under random bonds from the second-order regime of the pure model, has the same values of critical exponents as the two-dimensional Ising universality class, with the effect of the bond disorder on the specific heat being well described by double-logarithmic corrections, our findings thus supporting the marginal irrelevance of quenched bond randomness. On the other hand, the second-order transition, emerging under bond randomness from the first-order regime of the pure model, has a distinctive universality class with nu=1.30(6) and beta/nu=0.128(5). These results amount to a strong violation of universality principle of critical phenomena, since these two second-order transitions, with different sets of critical exponents, are between the same ferromagnetic and paramagnetic phases. Furthermore, the latter of these two sets of results supports an extensive but weak universality, since it has the same magnetic critical exponent (but a different thermal critical exponent) as a wide variety of two-dimensional systems with and without quenched disorder. In the conversion by bond randomness of the first-order transition of the pure system to second order, we detect, by introducing and evaluating connectivity spin densities, a microsegregation that also explains the increase we find in the phase transition temperature under bond randomness.
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    PublicationOpen Access
    Inverted Berezinskii-Kosterlitz-Thouless singularity and high-temperature algebraic order in an Ising model on a scale-free hierarchical-lattice small-world network
    (American Physical Society (APS), 2006) Hinczewski, Michael; Department of Physics; Department of Physics; Berker, Ahmet Nihat; Faculty Member; College of Sciences
    We have obtained exact results for the Ising model on a hierarchical lattice incorporating three key features characterizing many real-world networks-a scale-free degree distribution, a high clustering coefficient, and the small-world effect. By varying the probability p of long-range bonds, the entire spectrum from an unclustered, non-small-world network to a highly clustered, small-world system is studied. Using the self-similar structure of the network, we obtain analytic expressions for the degree distribution P(k) and clustering coefficient C for all p, as well as the average path length center dot for p=0 and 1. The ferromagnetic Ising model on this network is studied through an exact renormalization-group transformation of the quenched bond probability distribution, using up to 562 500 renormalized probability bins to represent the distribution. For p < 0.494, we find power-law critical behavior of the magnetization and susceptibility, with critical exponents continuously varying with p, and exponential decay of correlations away from T-c. For p >= 0.494, in fact where the network exhibits small-world character, the critical behavior radically changes: We find a highly unusual phase transition, namely an inverted Berezinskii-Kosterlitz-Thouless singularity, between a low-temperature phase with nonzero magnetization and finite correlation length and a high-temperature phase with zero magnetization and infinite correlation length, with power-law decay of correlations throughout the phase. Approaching T-c from below, the magnetization and the susceptibility, respectively, exhibit the singularities of exp(-C/root T-c-T) and exp(D/root T-c-T), with C and D positive constants. With long-range bond strengths decaying with distance, we see a phase transition with power-law critical singularities for all p, and evaluate an unusually narrow critical region and important corrections to power-law behavior that depend on the exponent characterizing the decay of long-range interactions.