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Photonic bound states in the continuum are spatially localised modes with infinitely long lifetimes that exist within a radiation continuum at discrete energy levels. These states have been explored in various systems where their emergence…
The bending energy of any freely deformable closed surface is quadratic in its curvature. In the absence of constraints, it will be minimized when the surface adopts the form of a round sphere. If the surface is confined within a…
Looking for a quantum-mechanical implementation of duality, we formulate a relation between coherent states and complex-differentiable structures on classical phase space ${\cal C}$. A necessary and sufficient condition for the existence of…
Physical systems in real life are inextricably linked to their surroundings and never completely separated from them. Truly closed systems do not exist. The phenomenon of decoherence, which is brought about by the interaction with the…
The eigenvalue of the hermitic Hamiltonian is real undoubtedly. Actually, The reality can also be guaranteed by the $PT$-symmetry. The hermiticity and the $PT$-symmetric quantum theory both have requirements regarding the boundary…
Bekenstein has presented evidence for the existence of a universal upper bound of magnitude $2\pi R/\hbar c$ to the entropy-to-energy ratio $S/E$ of an arbitrary {\it three} dimensional system of proper radius $R$ and negligible…
We prove a lower bound on the relative entropy between two finite-dimensional states in terms of their entropy difference and the dimension of the underlying space. The inequality is tight in the sense that equality can be attained for any…
Due to conservation of energy we cannot directly turn a quantum system with a definite energy into a superposition of different energies. However, if we have access to an additional resource in terms of a system with a high degree of…
Numerous quantum many-body systems are characterized by either fundamental or emergent constraints---such as gauge symmetries or parity superselection for fermions---which effectively limit the accessible observables and realizable…
Quantum ergodicity theorem states that for quantum systems with ergodic classical flows, eigenstates are, in average, uniformly distributed on energy surfaces. We show that if N is a hypersurface in the position space satisfying a simple…
Based on the modelling of quantum systems with the aid of (classical) non-equilibrium thermodynamics, both the emergence and the collapse of the superposition principle are understood within one and the same framework. Both are shown to…
Quantum states naturally decay under noise. Many earlier works have quantified and demonstrated lower bounds on the decay rate, showing exponential decay in a wide variety of contexts. Here we study the converse question: are there uniform…
A bipartite quantum state (for two systems in any dimensions) can be decomposed as a superposition of many components. For a superposition of more than two components we prove that there is a bound of the entanglement of the superposition…
Quantum backflow is the classically-forbidden effect pertaining to the fact that a particle with a positive momentum may exhibit a negative probability current at some space-time point. We investigate how this peculiar phenomenon extends to…
There has been much recent work on quantum inequalities to constrain negative energy. These are uncertainty principle-type restrictions on the magnitude and duration of negative energy densities or fluxes. We consider several examples of…
Quantum interferences between non-orthogonal states are the best approximation of a joint realization of the non-commuting physical properties represented by the two states. As I have shown recently, such interferences can be used to…
We consider a family of open sets $M_\epsilon$ which shrinks with respect to an appropriate parameter $\epsilon$ to a graph. Under the additional assumption that the vertex neighbourhoods are small we show that the appropriately shifted…
The imposition of boundary conditions upon a quantized field can lead to singular energy densities on the boundary. We treat the boundaries as quantum mechanical objects with a nonzero position uncertainty, and show that the singular energy…
We introduce a nonequilibrium phenomenon, reminiscent of Anderson's orthogonality catastrophe (OC), that arises in the transient dynamics following an interaction quench between a quantum system and a localized defect. Even if the system…
We demonstrate by an explicit model calculation that the decay of entanglement of two two-state systems (two qubits) is governed by the product of the factors that measure the degree of decoherence of each of the qubits, subject to…