N=2 supersymmetry and anisotropic scale invariance

Abstract

We find a class of scale-anomaly-free N ¼ 2 supersymmetric quantum systems with nonvanishing potential terms where space and time scale with distinct exponents. Our results generalize the known case of the supersymmetric inverse square potential to a larger class of scaling symmetries.

A New Version of the Aharonov–Bohm Effect

“…Such choice corresponds, mathematically, to the choice of a self-adjoint extension of the initial magnetic Hamiltonian, since usually the preliminary physical information provides only a symmetric operator; the self-adjoint property is required (in fact equivalent) for a unitary time evolution (conservation of probability) in quantum dynamics. The topic is related to the existence of anomalies [13], the presence of anisotropic scale invariances [14], different surface spectra of Weyl semimetals [35], creation of a pointlike source in quantum field theory [39], studies of topological quantum phases [3] and models in quantum gravity whose time evolution depend on boundary conditions at the origin [28], to mention only a handful of examples that illustrate the well-known fact that different self-adjoint extensions correspond to different physics. An instructive discussion about self-adjoint extensions of the simple case of a particle in a potential well appears in [12].…”

On the landscape of scale invariance in quantum mechanics

“…Thus, a quantum phase transition occurs at λ c between a CSI phase and a DSI phase. This transition has been associated with Berezinskii-Kosterlitz-Thouless (BKT) transitions [13,[17][18][19][20][21][22] and has found applications in the Efimov effect [23][24][25], graphene [14], QED3 [26] and other phenomena [17,[27][28][29][30][31][32][33][34].…”

“…This feature is a signature of residual DSIThus, * danny.brattan@gmail.com † somrie@campus.technion.ac.il ‡ eric@physics.technion.ac.il a quantum phase transition occurs at λ c between a continuous scale invariant (CSI) phase and a discrete scale invariant phase (DSI). This transition has been associated with Berezinskii-Kosterlitz-Thouless (BKT) transitions [13, 18-23] and has found applications in the Efimov effect [24-26], graphene [15], QED3 [27] and other phenomena [18,[28][29][30][31][32][33][34][35].A useful tool in the characterisation of this phenomenon is the renormalisation group (RG) [36]. For the case ofĤ S,D,L , it consists of introducing an initial short distance scale L and defining model dependent parameters such as λ, and the boundary conditions, according to physical information.…”

“…Thus, a quantum phase transition occurs at λ c between a continuous scale invariant (CSI) phase and a discrete scale invariant phase (DSI). This transition has been associated with Berezinskii-Kosterlitz-Thouless (BKT) transitions [13,[18][19][20][21][22][23] and has found applications in the Efimov effect [24][25][26], graphene [15], QED3 [27] and other phenomena [18,[28][29][30][31][32][33][34][35]. A useful tool in the characterisation of this phenomenon is the renormalisation group (RG) [36].…”