Research Outputs

Permanent URI for this communityhttps://hdl.handle.net/20.500.14288/2

Browse

Filters

Advanced Search

Filter by

Settings

Sponsors: search.filters.sponsors.N/ASubject: search.filters.subject.Mathematical physics

Search Results

Now showing 1 - 10 of 27
  • Thumbnail Image
    PublicationOpen 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; Sayar, Mehmet; Faculty Member; Department of Mechanical Engineering; College of Engineering; 109820
    The 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.
  • Thumbnail Image
    PublicationOpen Access
    Calculating the local solvent chemical potential in crystal hydrates
    (American Physical Society (APS), 2000) Mezei, M.; Department of Chemical and Biological Engineering; Reşat, Haluk; Faculty Member; Department of Chemical and Biological Engineering; College of Engineering
    Determining solvation patterns in biological systems is crucial in investigating the functional role water may play in structural stabilization and molecular recognition. Determining whether a particular position would be occupied by a solvent molecule requires the local thermodynamics to be known. In this work we introduce a simple and inexpensive approach based on grand canonical molecular simulations to determine the occupancy factors of the cavities. The method is applied to the test case of the sodium salt of hyaluronic acid. The results agree very well with experimental results and demonstrate the success of the method.
  • Thumbnail Image
    PublicationOpen 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; Mostafazadeh, Ali; Faculty Member; Department of Mathematics; College of Sciences; 4231
    For 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.
  • Thumbnail Image
    PublicationOpen Access
    Is weak pseudo-Hermiticity weaker than pseudo-Hermiticity?
    (American Institute of Physics (AIP) Publishing, 2006) Department of Mathematics; Mostafazadeh, Ali; Faculty Member; Department of Mathematics; College of Sciences; 4231
    For a weakly pseudo-Hermitian linear operator, we give a spectral condition that ensures its pseudo-Hermiticity. This condition is always satisfied whenever the operator acts in a finite-dimensional Hilbert space. Hence weak pseudo-Hermiticity and pseudo-Hermiticity are equivalent in finite-dimensions. This equivalence extends to a much larger class of operators. Quantum systems whose Hamiltonian is selected from among these operators correspond to pseudo-Hermitian quantum systems possessing certain symmetries.
  • Thumbnail Image
    PublicationOpen Access
    Junction formation during desiccation cracking
    (American Physical Society (APS), 2006) Toga, K. B.; Department of Mechanical Engineering; Alaca, Burhanettin Erdem; Faculty Member; Department of Mechanical Engineering; College of Engineering; 115108
    In order to provide a sound physical basis for the understanding of the formation of desiccation crack networks, an experimental study is presented addressing junction formation. Focusing on junctions, basic features of the network determining the final pattern, provides an elemental approach and imparts conceptual clarity to the rather complicated problem of the evolution of crack patterns. Using coffee-water mixtures a clear distinction between junction formation during nucleation and propagation is achieved. It is shown that for the same drying suspension, one can switch from the well-known symmetric triple junctions that are unique to the nucleation phase to propagation junctions that are purely dictated by the variations of the stress state. In the latter case, one can even manipulate the path of a propagating crack in a deterministic fashion by changing the stress state within the suspension. Clear microscopic evidence is provided for the formation of propagation junctions, and material inhomogeneity is observed to be reflected by a broad distribution of angles, in stark contrast to shrinkage cracks in homogeneous solid films.
  • Thumbnail Image
    PublicationOpen Access
    Lyapunov exponents for classical-quantum mixed-mode dynamics
    (American Physical Society (APS), 1996) Department of Chemistry; Yurtsever, İsmail Ersin; Researcher; Department of Chemistry; College of Sciences; 7129
    The mixed-mode philosophy of combining classical and quantum degrees of freedom under a single umbrella is employed to study chaotic behavior under quantization. The quantal wave packet is expanded in terms of a set of basis functions. The Jacobi-Hamilton formalism of the time-dependent Schrodinger equation allows the treatment of real and imaginary components of the time-dependent expansion coefficients as coordinates and momenta so that Lyapunov exponents can be calculated. Under the mixed-mode formalism, a two-dimensional nonlinearly coupled oscillator system is partially quantized by letting one of the modes obey classical and the other quantal dynamics. The Lyapunov exponent spectrum of the complete system is obtained and the results are compared with the fully classical ones.
  • Thumbnail Image
    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; Müstecaplıoğlu, Özgür Esat; Kiraz, Alper; Faculty Member; Faculty Member; Department of Physics; 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.
  • Thumbnail Image
    PublicationOpen Access
    Percolation transition in a dynamically clustered network
    (American Physical Society (APS), 2007) Zen, A.; Stella, A. L.; Department of Physics; Kabakçıoğlu, Alkan; Faculty Member; Department of Physics; College of Sciences; 49854
    We consider a percolationlike phenomenon on a generalization of the Barabasi-Albert model, where a modification of the growth dynamics directly allows formation of disconnected clusters. The transition is located with high precision by an original numerical technique based on the comparison of the largest and second largest clusters. A careful investigation focusing on finite size scaling allows us to highlight properties which would hardly be accessible by an analytical solution of cluster growth equations in the stationary limit. Our analysis shows that some critical features of the percolation transition are different from those observed in the case of dilution in fully grown networks. At variance with other models of percolation on growing networks we also find evidence that the order parameter approaches zero as a power of the field p-p(c) driving the transition, rather than as a stretched exponential. This behavior does not agree with the Berezinskii-Kosterlitz-Thouless scenario found in other similar models. For describing the phase in which a giant cluster develops, a key role is played by the crossover number of nodes N-x similar to(p-p(c))(-zeta) with zeta similar or equal to 4. This power law behavior and that of other quantities are conjectured on the basis of scaling arguments and numerical evidence.
  • Thumbnail Image
    PublicationOpen Access
    Propagation of short pulses through a Bose-Einstein condensate
    (Institute of Physics (IOP) Publishing, 2006) Tarhan, Devrim; Sefi, Seckin; Department of Physics; Müstecaplıoğlu, Özgür Esat; Faculty Member; Department of Physics; College of Sciences; 1674
    We study propagation of short laser pulses in a Bose-Einstein condensate taking into account dispersive effects under the conditions for electromagnetically induced transparency. We calculate dispersion coefficients using typical experimental parameters of slow-light schemes in condensates. By numerically propagating the laser pulse, and referring to theoretical estimations, we determine the conditions for which dispersion starts to introduce distortions on the pulse shape.
  • Thumbnail Image
    PublicationOpen Access
    Pseudo-Hermiticity and generalized PT- and CPT-symmetries
    (American Institute of Physics (AIP) Publishing, 2003) Department of Mathematics; Mostafazadeh, Ali; Faculty Member; Department of Mathematics; College of Sciences; 4231
    We study certain linear and antilinear symmetry generators and involution operators associated with pseudo-Hermitian Hamiltonians and show that the theory of pseudo-Hermitian operators provides a simple explanation for the recent results of Bender, Brody and Jones (quant-ph/0208076) on the CPT-symmetry of a class of PT-symmetric non-Hermitian Hamiltonians. We present a natural extension of these results to the class of diagonalizable pseudo-Hermitian Hamiltonians H with a discrete spectrum. In particular, we introduce generalized parity (P), time-reversal (T), and charge-conjugation (C) operators and establish the PT- and CPT-invariance of H.