Related papers: PT-symmetric quantum mechanics
Brief review is given of my recent results on solvable models within the so called PT symmetric version of quantum mechanics.
The Hermiticity axiom of quantum mechanics guarantees that the energy spectrum is real and the time evolution is unitary (probability-preserving). Nevertheless, non-Hermitian but $\mathcal{PT}$-symmetric Hamiltonians may also have real…
PT-symmetric systems can have a real spectrum even when their Hamiltonian is non-hermitian, but develop a complex spectrum when the degree of non-hermiticity increases. Here we utilize random-matrix theory to show that this spontaneous…
A new method to work out the Hermitian correspondence of a PT-symmetric quantum mechanical Hamiltonian is proposed. In contrast to the conventional method, the new method ends with a local Hamiltonian of the form p^2/2+m^2x^2/2+v(x) without…
We explain why the main conclusion of Bender et al, hep-th/0511229 [J. Phys. A 39 (2006) 1657] regarding the practical superiority of the non-Hermitian description of PT-symmetric quantum systems over their Hermitian description is not…
In recent decades, an important shift has taken place with the growing role of non-Hermitian quantum mechanics. What makes this framework remarkable is that the eigenvalues of the Hamiltonians involved can still be real, just as in the…
We find that a broken PT-symmetry operator when interacts with suitable Hermitian operator, new system becomes completely un-broken PT symmetry. Further on varying the contribution of Hermiticity one can delay or control the broken…
If a Hamiltonian is PT symmetric, there are two possibilities: Either the eigenvalues are entirely real, in which case the Hamiltonian is said to be in an unbroken-PT-symmetric phase, or else the eigenvalues are partly real and partly…
The Hamiltonian H specifies the energy levels and time evolution of a quantum theory. A standard axiom of quantum mechanics requires that H be Hermitian because Hermiticity guarantees that the energy spectrum is real and that time evolution…
A quantum-mechanical theory is PT-symmetric if it is described by a Hamiltonian that commutes with PT, where the operator P performs space reflection and the operator T performs time reversal. A PT-symmetric Hamiltonian often has a…
The concept of parity-time (PT) symmetry originates from the framework of quantum mechanics, where if the Hamiltonian operator satisfies the commutation relation with the parity and time operators, it shows all real eigen-energy spectrum.…
A defining quantity of a physical system is its energy which is represented by the Hamiltonian. In closed quantum mechanical or/and coherent wave-based systems the Hamiltonian is introduced as a Hermitian operator which ensures real energy…
The physics of systems that cannot be described by a Hermitian Hamiltonian, has been attracting a great deal of attention in recent years, motivated by their nontrivial responses and by a plethora of applications for sensing, lasing, energy…
Two non-Hermitian PT-symmetric Hamiltonian systems are reconsidered by means of the algebraic method which was originally proposed for the pseudo-Hermitian Hamiltonian systems rather than for the PT-symmetric ones. Compared with the way…
For a subclass of a general $\mathcal{PT}-$symmetric Hamiltonian obeying anti-commutation relation with its conjugate, a Hermitian basis is found that spans the bi-orthonormal energy eigenvectors. Using the modified projectors constructed…
A condition to have a real spectrum for a non-Hermitian Hamiltonian is given. As special cases, it is shown that the condition is reduced to Hermiticity and PT symmetric conditions.
The author discusses a different kind of Hermitian quantum mechanics, called $J$-Hermitian quantum mechanics. He shows that $PT$-symmetric quantum mechanics is indeed $J$-Hermitian quantum mechanics, and that time evolution (in the Krein…
Suppose that a system is known to be in one of two quantum states, $|\psi_1 > $ or $|\psi_2 >$. If these states are not orthogonal, then in conventional quantum mechanics it is impossible with one measurement to determine with certainty…
$\mathcal{PT}$-symmetric quantum mechanics has been considered an important theoretical framework for understanding physical phenomena in $\mathcal{PT}$-symmetric systems, with a number of $\mathcal{PT}$-symmetry related applications. This…
The quantum-field model described by non-Hermitian, but a ${\cal PT}$-symmetric Hamiltonian is considered. It is shown by the algebraic way that the limiting of the physical mass value $m \leq m_{max}= {m_1}^2/2m_2$ takes place for the case…