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In ${\cal PT}-$symmetric quantum mechanics one of the most characteristic mathematical features of the formalism is the explicit Hamiltonian-dependence of the physical Hilbert space of states ${\cal H}={\cal H}(H)$. Some of the most…

Quantum Physics · Physics 2018-03-20 Miloslav Znojil

A PT-symmetric Bose-Einstein condensate can be theoretically described using a complex optical potential, however, the experimental realization of such an optical potential describing the coherent in- and outcoupling of particles is a…

Quantum Physics · Physics 2013-05-08 Manuel Kreibich , Jörg Main , Holger Cartarius , Günter Wunner

The "Hermitizability" problem of quantum theory is explained, discussed and illustrated via the discrete-lattice cryptohermitian quantum graphs. In detail, the description of the domain ${\cal D}$ of admissible parameters is provided for…

Quantum Physics · Physics 2012-01-16 Miloslav Znojil

Within CPT-symmetric quantum mechanics the most elementary differential form of the charge operator C is assumed. A closed-form integrability of the related coupled differential self-consistency conditions and a natural embedding of the…

Mathematical Physics · Physics 2009-05-18 Emanuela Caliceti , Francesco Cannata , Miloslav Znojil , Alberto Ventura

PT-symmetric quantum mechanics is an alternative formulation of quantum mechanics in which the mathematical axiom of Hermiticity (transpose and complex conjugate) is replaced by the physically transparent condition of space-time reflection…

Mathematical Physics · Physics 2015-06-12 Huai-Xin Cao , Zhi-Hua Guo , Zheng-Li Chen

A new version of an elementary PT-symmetric square well quantum model is proposed in which a certain Hermiticity-violating end-point interaction leaves the spectrum real in a large domain of couplings $\lambda\in (-1,1)$. Within this…

Quantum Physics · Physics 2011-07-13 Miloslav Znojil , Miloš Tater

A $\mathcal{PT}$-symmetric, non-Hermitian Hamiltonian in the $\mathcal{PT}$-unbroken regime can lead to unitary dynamics under the appropriate choice of the Hilbert space. The Hilbert space is determined by a Hamiltonian-compatible inner…

Quantum Physics · Physics 2025-03-19 Himanshu Badhani , Subhashish Banerjee , C. M. Chandrashekar

The occurrence of parity-time reversal ($\mathcal{PT}$) symmetry breaking is discussed in a non-Hermitian spin chain. The Hermiticity of the model is broken by the presence of an alternating, imaginary, transverse magnetic field. A full…

Quantum Physics · Physics 2010-08-25 Gian Luca Giorgi

Real-to-complex spectral transitions and the associated spontaneous symmetry breaking of eigenstates are central to non-Hermitian physics, yet a comprehensive and universal theory that precisely describes the underlying physical mechanisms…

Quantum Physics · Physics 2025-06-23 Zhuo-Ting Cai , Hai-Dong Li , Wei Chen

The simplest purely imaginary and piecewise constant $\cal PT$-symmetric potential located inside a larger box is studied. Unless its strength exceeds a certain critical value, all the spectrum of its bound states remains real and discrete.…

Quantum Physics · Physics 2016-12-22 B. Bagchi , H. Bila , V. Jakubsky , S. Mallik , C. Quesne , M. Znojil

Analytically solvable models are benchmarks in studies of phase transitions and pattern-forming bifurcations. Such models are known for phase transitions of the second kind in uniform media, but not for localized states (solitons), as…

Pattern Formation and Solitons · Physics 2023-08-17 Shatrughna Kumar , Pengfei Li , Liangwei Zeng , Jingsong He , Boris A. Malomed

Balanced gain and loss leads to stationary dynamics in open systems. This occurs naturally in PT-symmetric systems, where the imaginary part of the potential describing gain and loss is perfectly antisymmetric. While this case seems…

Quantum Physics · Physics 2020-09-22 Daniel Dizdarevic , Holger Cartarius , Jörg Main , Günter Wunner

Unavoided crossings of the energy levels due to a variation of a real parameter are studied. It is found that after the quantum system in question passes through one of its energy-crossing points {\it alias} Kato's exceptional points (EP),…

Quantum Physics · Physics 2016-07-05 Denis I. Borisov , Miloslav Znojil

The Parity-Time ($\mathcal{PT}$) symmetric potentials are derived by non-Hermitian supersymmetric quantum mechanics for square well and barrier. These $\mathcal{PT}$-supersymmetric square well and barrier. The partners have complex…

Quantum Physics · Physics 2020-01-28 Taha Koohrokhi

We construct PT-symmetric quantum mechanical models with an O(N)-symmetric interaction term of the form $-g(\vec{x}^{2})^{2}/N$. Using functional integral methods, we find the equivalent Hermitian model, which has several unusual features.…

High Energy Physics - Theory · Physics 2007-07-12 Peter N. Meisinger , Michael C. Ogilvie

Parity-time (PT) symmetry has attracted a lot of attention since the concept of pseudo-Hermitian dynamics of open quantum systems was first demonstrated two decades ago. Contrary to their Hermitian counterparts, non-conservative…

Generalized PT symmetry provides crucial insight into the sign problem for two classes of models. In the case of quantum statistical models at non-zero chemical potential, the free energy density is directly related to the ground state…

High Energy Physics - Theory · Physics 2010-09-06 Peter N. Meisinger , Michael C. Ogilvie , Timothy D. Wiser

Closed expressions are derived for the pseudo-norm, norm and orthogonality relations for arbitrary bound states of the PT symmetric and the Hermitian Scarf II potential for the first time. The pseudo-norm is found to have indefinite sign in…

Quantum Physics · Physics 2009-11-07 G. Levai , F. Cannata , A. Ventura

We investigate particular models which can be N-fold supersymmetric at specific values of a parameter in the Hamiltonians. The models to be investigated are a periodic potential and a parity-symmetric sextic triple-well potential. Through…

High Energy Physics - Theory · Physics 2009-11-07 Masatoshi Sato , Toshiaki Tanaka

We briefly explain some simple arguments based on pseudo Hermiticity, supersymmetry and PT-symmetry which explain the reality of the spectrum of some non-Hermitian Hamiltonians. Subsequently we employ PT-symmetry as a guiding principle to…

Quantum Physics · Physics 2008-04-17 Andreas Fring