相关论文: Near-Schr\"odinger dynamics at large charge
The large-charge master field which generates all n-point correlation functions with an insertion of large charge Q in non-relativistic conformal field theory is obtained. This field is used to compute Schr\"odinger-invariant n-point…
We investigate four-dimensional near-conformal dynamics by means of the large-charge limit. We first introduce and justify the formalism in which near-conformal invariance is insured by adding a dilaton and then determine the large-charge…
In this note, we perform the large-charge expansion for non-relativistic systems with a global $U(1)$ symmetry in $3+1$ and $2+1$ space-time dimensions, motivated by applications to the unitary Fermi gas and anyons. These systems do not…
We study Schr\"odinger invariant field theories (nonrelativistic conformal field theories) in the large charge (particle number) sector. We do so by constructing the effective field theory (EFT) for a Goldstone boson of the associated…
The unitary Fermi gas, by virtue of its description as a nonrelativistic conformal field theory, has proven an interesting system by which the quantum properties of CFT can be held to experimental verification. Here, we examine the…
Nonlinearities in the dispersion relations associated with different interactions designs, boundary conditions and the existence of a physical cut-off scale can alter the quantum vacuum energy of a nonrelativistic system nontrivially. As a…
We extend and clarify the large-charge expansion of the conformal dimension $\Delta_Q$ of the lowest operator of charge $Q$ in nonrelativistic CFTs using the state-operator correspondence. The latter requires coupling the theory to an…
We study operators in Schr\"odinger invariant field theories (non-relativistic conformal field theories or NRCFTs) with large charge (particle number) and spin. Via the state-operator correspondence for NRCFTs, such operators correspond to…
We consider the large-charge expansion of the charged ground state of a Schrodinger-invariant, nonrelativistic conformal field theory in a harmonic trap, in general dimension d. In the existing literature, the energy in the trap has been…
It is shown that the Schr\"{o}dinger equation for a system of interacting particles whose Compton wavelengths are of the same order of magnitude as the system size is contradictory and is not strictly nonrelativistic, because it is based on…
Conformal field theories (CFTs) are associated with critical phenomena and phase transitions and also play an essential role in string theory. Solving a CFT is an extremely constrained problem due to conformal invariance -- the task…
The multi-critical behaviour of an approximately scale and conformal invariant quantum field theory, which can be regarded as the deformation of the critical Gross-Neveu model in 3+epsilon dimensions by a nearly marginal parity violating…
In this work we study a system of Schr\"odinger equations involving nonlinearities with quadratic growth. We establish sharp criterion concerned with the dichotomy global existence versus blow-up in finite time. Such a criterion is given in…
In this paper, we study the solutions to the energy-critical quadratic nonlinear Schr\"odinger system in ${\dot H}^1\times{\dot H}^1$, where the sign of its potential energy can not be determined directly. If the initial data ${\rm u}_0$ is…
Considering theories in sectors of large global charge $Q$ results in a semiclassical effective field theory (EFT) description for some strongly-coupled conformal field theories (CFTs) with continuous global symmetries. Hence, when studying…
Incompressibility plays a key role in the geometric description of fractional quantum Hall fluids. It is naturally related to quantum area-preserving diffeomorphisms and the underlying Girvin-MacDonald-Plazman algebra, which gives rise to…
From the mathematical side, nonlinear Schr\"odinger equations are usually investigated via variational methods, that cease to work in higher dimensions. This thesis tries to overcome this problem by focusing on spherically symmetric…
I examine a model for the Hall effect in the strongly correlated regime. It emerges from an approach proposed in my previous articles [e.g. J. Phys. Chem. Solids, 65 (2004), 1507-1515; J. Geom. Phys., in press, cf. math-ph/0409023]. The…
Charge fractionalization is the phenomenon where quasi-particle excitations in a many-particle system appear with non-integer values relative to the fundamental charge unit. Examples of such systems are known from field theoretical models…
From non-linear theory of electromagnetism, suggested in (physics/9801031), follows that non-relativistic equation for scalar potential of electron in the field of nuclei is equivalent to respective Schr\"odinger equation. For mass and…