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

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Now showing 1 - 10 of 26
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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
    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; 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.
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    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; Department of Mechanical Engineering; Sayar, Mehmet; Faculty Member; 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.
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    PublicationOpen 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; 4231
    We 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.
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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
    Pseudo-Hermiticity versus PT symmetry: the necessary condition for the reality of the spectrum of a non-Hermitian Hamiltonian
    (American Institute of Physics (AIP) Publishing, 2002) Department of Mathematics; Department of Mathematics; Mostafazadeh, Ali; Faculty Member; College of Sciences; 4231
    We introduce the notion of pseudo-Hermiticity and show that every Hamiltonian with a real spectrum is pseudo-Hermitian. We point out that all the PT-symmetric non-Hermitian Hamiltonians studied in the literature belong to the class of pseudo-Hermitian Hamiltonians, and argue that the basic structure responsible for the particular spectral properties of these Hamiltonians is their pseudo-Hermiticity. We explore the basic properties of general pseudo-Hermitian Hamiltonians, develop pseudosupersymmetric quantum mechanics, and study some concrete examples, namely the Hamiltonian of the two-component Wheeler-DeWitt equation for the FRW-models coupled to a real massive scalar field and a class of pseudo-Hermitian Hamiltonians with a real spectrum.
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    PublicationOpen Access
    Lyapunov exponents for classical-quantum mixed-mode dynamics
    (American Physical Society (APS), 1996) Department of Chemistry; Department of Chemistry; Yurtsever, İsmail Ersin; Researcher; 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.
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    PublicationOpen Access
    Is weak pseudo-Hermiticity weaker than pseudo-Hermiticity?
    (American Institute of Physics (AIP) Publishing, 2006) Department of Mathematics; Department of Mathematics; Mostafazadeh, Ali; Faculty Member; 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.
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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
    Calculating the local solvent chemical potential in crystal hydrates
    (American Physical Society (APS), 2000) Mezei, M.; Department of Chemical and Biological Engineering; Department of Chemical and Biological Engineering; Reşat, Haluk; Faculty Member; 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.