Imperial College London

DrEva-MariaGraefe

Faculty of Natural SciencesDepartment of Mathematics

Research Fellow (Royal Society URF)
 
 
 
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Contact

 

+44 (0)20 7594 8549e.graefe CV

 
 
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Location

 

682Huxley BuildingSouth Kensington Campus

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Summary

 

Publications

Publication Type
Year
to

34 results found

Graefe EM, Longstaff B, Plastow T, Schubert Ret al., 2017, Lindblad dynamics of Gaussian states and their superpositions in the semiclassical limit

The time evolution of the Wigner function for Gaussian states generated byLindblad quantum dynamics is investigated in the semiclassical limit. A newtype of classical phase-space dynamics is obtained, where the Lindblad termsgenerally introduce a non-Hamiltonian flow. In addition to this classicalphase-space dynamics, the Gaussian approximation yields dynamical equations forthe covariances. The approximation becomes exact for linear Lindblad operatorsand a quadratic Hamiltonian. By viewing the Wigner function as a wave functionon a coordinate space of doubled dimension, and the phase-space Lindbladequation as a Schr\"{o}dinger equation with a non-Hermitian Hamiltonian, afurther set of semiclassical equations are derived. These are also capable ofdescribing the interference terms in Wigner functions arising in superpositionsof Gaussian states, as demonstrated for a cat state in an anharmonic oscillatorsubject to damping.

JOURNAL ARTICLE

Graefe E-M, Korsch HJ, Rush A, 2016, Classical-quantum correspondence in bosonic two-mode conversion systems: Polynomial algebras and Kummer shapes, PHYSICAL REVIEW A, Vol: 93, ISSN: 2469-9926

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Graefe E-M, Rush A, Schubert R, 2016, Propagation of Gaussian Beams in the Presence of Gain and Loss, IEEE JOURNAL OF SELECTED TOPICS IN QUANTUM ELECTRONICS, Vol: 22, ISSN: 1077-260X

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Graefe EM, Korsch HJ, Rush A, 2016, Quasiclassical analysis of Bloch oscillations in non- Hermitian tight-binding lattices, NEW JOURNAL OF PHYSICS, Vol: 18, ISSN: 1367-2630

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Graefe E-M, Graney M, Rush A, 2015, Semiclassical quantization for a bosonic atom-molecule conversion system, PHYSICAL REVIEW A, Vol: 92, ISSN: 1050-2947

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Graefe E-M, Mudute-Ndumbe S, Taylor M, 2015, Random matrix ensembles for $PT$-symmetric systems, Journal of Physics A - Mathematical and Theoretical, Vol: 48, ISSN: 1751-8113

Recently much effort has been made towards the introduction of non-Hermitianrandom matrix models respecting $PT$-symmetry. Here we show that there is aone-to-one correspondence between complex $PT$-symmetric matrices andsplit-complex and split-quaternionic versions of Hermitian matrices. Weintroduce two new random matrix ensembles of (a) Gaussian split-complexHermitian, and (b) Gaussian split-quaternionic Hermitian matrices, of arbitrarysizes. They are related to the split signature versions of the complex and thequaternionic numbers, respectively. We conjecture that these ensemblesrepresent universality classes for $PT$-symmetric matrices. For the case of$2\times2$ matrices we derive analytic expressions for the joint probabilitydistributions of the eigenvalues, the one-level densities and the levelspacings in the case of real eigenvalues.

JOURNAL ARTICLE

Graefe E-M, Korsch HJ, Rush A, Schubert Ret al., 2014, Classical and quantum dynamics in the (non-Hermitian) Swanson oscillator, Journal of Physics A-Mathematical and General, ISSN: 1361-6447

The non-Hermitian quadratic oscillator studied by Swanson is one of thepopular $PT$-symmetric model systems. Here a full classical description of itsdynamics is derived using recently developed metriplectic flow equations, whichcombine the classical symplectic flow for Hermitian systems with a dissipativemetric flow for the anti-Hermitian part. Closed form expressions for the metricand phase-space trajectories are presented which are found to be periodic intime. Since the Hamiltonian is only quadratic the classical dynamics exactlydescribes the quantum dynamics of Gaussian wave packets. It is shown that theclassical metric and trajectories as well as the quantum wave functions candiverge in finite time even though the $PT$-symmetry is unbroken, i.e., theeigenvalues are purely real.

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Graefe E-M, Korsch HJ, Strzys MP, 2014, Bose-Hubbard dimers, Viviani's windows and pendulum dynamics, JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, Vol: 47, ISSN: 1751-8113

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Brody DC, Graefe E-M, 2013, Information Geometry of Complex Hamiltonians and Exceptional Points, ENTROPY, Vol: 15, Pages: 3361-3378, ISSN: 1099-4300

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Graefe E-M, 2013, Quantum Chaos on Display, Physics, Vol: 6

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Graefe E-M, Liverani C, 2013, Mean-field approximation for a Bose-Hubbard dimer with complex interaction strength, JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, Vol: 46, ISSN: 1751-8113

JOURNAL ARTICLE

Graefe E-M, Mailybaev AA, Moiseyev N, 2013, Breakdown of adiabatic transfer of light in waveguides in the presence of absorption, PHYSICAL REVIEW A, Vol: 88, ISSN: 1050-2947

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Brody DC, Graefe E-M, 2012, Mixed-State Evolution in the Presence of Gain and Loss, PHYSICAL REVIEW LETTERS, Vol: 109, ISSN: 0031-9007

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Demange G, Graefe E-M, 2012, Signatures of three coalescing eigenfunctions, JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, Vol: 45, ISSN: 1751-8113

JOURNAL ARTICLE

Graefe E-M, 2012, Stationary states of a PT symmetric two-mode Bose-Einstein condensate, JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, Vol: 45, ISSN: 1751-8113

JOURNAL ARTICLE

Graefe E-M, Schubert R, 2012, Complexified coherent states and quantum evolution with non-Hermitian Hamiltonians, JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, Vol: 45, ISSN: 1751-8113

JOURNAL ARTICLE

Brody DC, Graefe E, 2011, Coquaternionic quantum dynamics for two-level systems, Acta Polytechnica: journal of advanced engineering, Vol: 51, Pages: 14-20

The dynamical aspects of a spin-1/2 particle in Hermitian coquaternionicquantum theory is investigated. It is shown that the time evolution exhibitsthree different characteristics, depending on the values of the parameters ofthe Hamiltonian. When energy eigenvalues are real, the evolution is eitherisomorphic to that of a complex Hermitian theory on a spherical state space, orelse it remains unitary along an open orbit on a hyperbolic state space. Whenenergy eigenvalues form a complex conjugate pair, the orbit of the timeevolution closes again even though the state space is hyperbolic.

JOURNAL ARTICLE

Brody DC, Graefe E-M, 2011, On complexified mechanics and coquaternions, JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, Vol: 44, ISSN: 1751-8113

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Brody DC, Graefe E-M, 2011, Six-dimensional space-time from quaternionic quantum mechanics, PHYSICAL REVIEW D, Vol: 84, ISSN: 1550-7998

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Graefe E-M, Jones HF, 2011, PT-symmetric sinusoidal optical lattices at the symmetry-breaking threshold, PHYSICAL REVIEW A, Vol: 84, ISSN: 1050-2947

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Graefe E-M, Schubert R, 2011, Wave-packet evolution in non-Hermitian quantum systems, PHYSICAL REVIEW A, Vol: 83, ISSN: 1050-2947

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Brody DC, Graefe E-M, 2010, Coherent states and rational surfaces, JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, Vol: 43, ISSN: 1751-8113

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Graefe E-M, Hoening M, Korsch HJ, 2010, Classical limit of non-Hermitian quantum dynamics-a generalized canonical structure, JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, Vol: 43, ISSN: 1751-8113

JOURNAL ARTICLE

Graefe E-M, Korsch HJ, Niederle AE, 2010, Quantum-classical correspondence for a non-Hermitian Bose-Hubbard dimer, PHYSICAL REVIEW A, Vol: 82, ISSN: 1050-2947

JOURNAL ARTICLE

Kolovsky AR, Korsch HJ, Graefe E-M, 2009, Bloch oscillations of Bose-Einstein condensates: Quantum counterpart of dynamical instability, PHYSICAL REVIEW A, Vol: 80, ISSN: 1050-2947

JOURNAL ARTICLE

Graefe EM, Guenther U, Korsch HJ, Niederle AEet al., 2008, A non-Hermitian PT symmetric Bose-Hubbard model: eigenvalue rings from unfolding higher-order exceptional points, JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, Vol: 41, ISSN: 1751-8113

JOURNAL ARTICLE

Graefe EM, Korsch HJ, Niederle AE, 2008, Mean-Field Dynamics of a Non-Hermitian Bose-Hubbard Dimer, PHYSICAL REVIEW LETTERS, Vol: 101, ISSN: 0031-9007

JOURNAL ARTICLE

Korsch HJ, Graefe EM, Jodl H-J, 2008, The kicked rotor: Computer-based studies of chaotic dynamics, AMERICAN JOURNAL OF PHYSICS, Vol: 76, Pages: 498-503, ISSN: 0002-9505

JOURNAL ARTICLE

Strzys MP, Graefe EM, Korsch HJ, 2008, Kicked Bose-Hubbard systems and kicked tops - destruction and stimulation of tunneling, NEW JOURNAL OF PHYSICS, Vol: 10, ISSN: 1367-2630

JOURNAL ARTICLE

Graefe EM, Korsch HJ, 2007, Semiclassical quantization of an N-particle Bose-Hubbard model, PHYSICAL REVIEW A, Vol: 76, ISSN: 1050-2947

JOURNAL ARTICLE

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