Network architecture of energy landscapes in mesoscopic quantum systems

Abstract

Mesoscopic quantum systems exhibit complex many-body quantum phenomena, where interactions between spins and charges give rise to collective modes and topological states. Even simple, noninteracting theories display a rich landscape of energy states-distinct many-particle configurations connected by spin-and energy-dependent transition rates. The ways in which these energy states interact is difficult to characterize or predict, especially in regimes of frustration where many-body effects create a multiply degenerate landscape. Here, we use network science to characterize the complex interconnection patterns of these energy-state transitions. Using an experimentally verified computational model of electronic transport through quantum antidots, we construct networks where nodes represent accessible energy states and edges represent allowed transitions. We find that these networks exhibit Rentian scaling, which is characteristic of efficient transportation systems in computer circuitry, neural circuitry, and human mobility, and can be used to measure the interconnection complexity of a network. We find that the topological complexity of the state transition networks-as measured by Rent's exponent-correlates with the amount of current flowing through the antidot system. Furthermore, networks corresponding to points of frustration (due, for example, to spin-blockade effects) exhibit an enhanced topological complexity relative to non-frustrated networks. Our results demonstrate that network characterizations of the abstract topological structure of energy landscapes capture salient properties of quantum transport. More broadly, our approach motivates future efforts to use network science to understand the dynamics and control of complex quantum systems. mesoscopic system and metallic reservoirs induce transitions between quantum-mechanical states, and these transitions can be detected through currents flowing in the device. Whether tunneling is allowed depends on the many-body configurations of the quantum system together with the spin and energy of electrons in the reservoirs.A quantum antidot exists as a hill in the electrostatic potential landscape of a two-dimensional electron system; see figure 1(A). Antidots exhibit discrete energy spectra due to magnetic confinement of electron orbital states, and they can be treated as 'dots of holes,' analogous to large quantum dots [5][6][7][8]. In devices, quantum antidots can be coupled to extended, propagating edge modes of the integer quantum Hall fluid, where the tunneling to discrete antidot states is controlled by external voltages; see figure 1(B). Whereas antidot transport near zero bias is typically dominated by a small number of energy states, the relevant number of states for nonequilibrium transport grows rapidly with the applied bias. The additional states relevant for non-equilibrium transport include excited states that result from different spin configurations and orbital excitations. The complexity of the interconnection patterns between these excited state...

Systemic Performance Measures from Distributional Zeta-Function

“…A natural continuation of this paper is to study other Euclidean models (such as Landau-Ginzburg model [87][88][89], Gross-Pitaevskii model [90][91][92], Euclidean Schwarzschild and other curved manifolds [93][94][95][96][97]) in order to obtain new elements for the set of DZF-based SPMs and extract out its advanges from its physical consequences. Another continuation is to evalue different phase transitions problems and entanglement networks of quantum systems of interets (such as qubits [98][99][100][101][102] or biological light-harvesting complexes [103][104][105][106][107]). Finally, the objects that we have constructed here can be used to study design, formation, growing, and robustness of real life networks to obtain a depper understanding of their complexity.…”

Response of quantum spin networks to attacks

“…via perturbation theory. This third scenario has already been explored in experiments on electronic transport through quantum antidots [29]; and in an open quantum system the system can be simple with a complex environment, or vice-versa [30].…”