Topological phases in non-Hermitian systems extend the traditional understanding of topological phases by considering systems where the Hamiltonian is not Hermitian, often due to the inclusion of gain and loss processes. These systems offer novel and rich physical phenomena like exceptional points and unique edge states, which have potential applications in photonics and quantum systems.

Topological Phases In Non-Hermitian Systems

Topological phases are states of matter that extend beyond the traditional classification based on symmetry breaking and are characterized by topological invariants that remain unchanged under continuous deformations. These phases exhibit robust edge states and exotic quantum phenomena, such as the quantum Hall effect, that are protected by the system's topology rather than its symmetry.

Topological Phases

Non-Hermitian systems extend the realm of quantum mechanics by considering Hamiltonians that are not Hermitian, allowing for the modeling of open systems where energy exchange with the environment occurs. These systems are characterized by complex eigenvalues, which can depict dissipative phenomena and exotic states such as exceptional points and non-Hermitian skin effects.

Non-Hermitian Systems

Traditional understanding of topological phases

The Hamiltonian is a fundamental operator in quantum mechanics that describes the total energy of a system, encompassing both kinetic and potential energy components. It plays a crucial role in Schrödinger's equation, determining how quantum states evolve over time.

Hamiltonian

Gain and loss processes

Novel physical phenomena

Exceptional points are singularities in the parameter space of non-Hermitian systems where two or more eigenvalues and their corresponding eigenvectors coalesce. They are critical in understanding phenomena such as phase transitions in non-Hermitian quantum mechanics and enhanced sensitivity in optical systems.

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