Springer Science and Business Media LLC
0010-3616
1432-0916
Cơ quản chủ quản: Springer New York , SPRINGER
Lĩnh vực:
Mathematical PhysicsStatistical and Nonlinear Physics
Phân tích ảnh hưởng
Thông tin về tạp chí
Các bài báo tiêu biểu
On the Strong Coupling Limit of the Faddeev-Hopf Model
- 2007
The variational calculus for the Faddeev-Hopf model on a general Riemannian domain, with general Kähler target space, is studied in the strong coupling limit. In this limit, the model has key similarities with pure Yang-Mills theory, namely conformal invariance in dimension 4 and an infinite dimensional symmetry group. The first and second variation formulae are calculated and several examples of stable solutions are obtained. In particular, it is proved that all immersive solutions are stable. Topological lower energy bounds are found in dimensions 2 and 4. An explicit description of the spectral behaviour of the Hopf map
$${S^3 \rightarrow S^2}$$
is given, and a conjecture of Ward concerning the stability of this map in the full Faddeev-Hopf model is proved.
Quantum Ergodicity for Periodic Graphs
Tập 403 - Trang 1477-1509 - 2023
This article shows that for a large class of discrete periodic Schrödinger operators, most wavefunctions resemble Bloch states. More precisely, we prove quantum ergodicity for a family of periodic Schrödinger operators H on periodic graphs. This means that most eigenfunctions of H on large finite periodic graphs are equidistributed in some sense, hence delocalized. Our results cover the adjacency matrix on
$$\mathbb {Z}^d$$
, the triangular lattice, the honeycomb lattice, Cartesian products, and periodic Schrödinger operators on
$$\mathbb {Z}^d$$
. The theorem applies more generally to any periodic Schrödinger operator satisfying an assumption on the Floquet eigenvalues.
A spherically symmetric solution of the Maxwell-Einstein equations
- 1967
A spherically symmetric solution of the “already unified field theory” ofRainich (i.e. of the source-free Maxwell-Einstein equations) is presented which represents a static massless charged particle. It is not equivalent to the Reissner-Nordström solution with zero mass, although both metrics repel uncharged test particles.
Rigorous Solution of Strongly Coupled SO(N) Lattice Gauge Theory in the Large N Limit
Tập 366 - Trang 203-268 - 2019
The main result of this paper is a rigorous computation of Wilson loop expectations in strongly coupled SO(N) lattice gauge theory in the large N limit, in any dimension. The formula appears as an absolutely convergent sum over trajectories in a kind of string theory on the lattice, demonstrating an explicit gauge-string duality. The generality of the proof technique may allow it to be extended other gauge groups.
Einige Bemerkungen zur Zustandsänderung von relativistischen quantenmechanischen Systemen durch Messungen und zur Lokalitätsforderung
Tập 7 Số 4 - Trang 305-331 - 1968
3XOR Games with Perfect Commuting Operator Strategies Have Perfect Tensor Product Strategies and are Decidable in Polynomial Time
Tập 400 - Trang 731-791 - 2023
We consider 3XOR games with perfect commuting operator strategies. Given any 3XOR game, we show existence of a perfect commuting operator strategy for the game can be decided in polynomial time. Previously this problem was not known to be decidable. Our proof leads to a construction, showing a 3XOR game has a perfect commuting operator strategy iff it has a perfect tensor product strategy using a 3 qubit (8 dimensional) GHZ state. This shows that for perfect 3XOR games the advantage of a quantum strategy over a classical strategy (defined by the quantum-classical bias ratio) is bounded. This is in contrast to the general 3XOR case where the optimal quantum strategies can require high dimensional states and there is no bound on the quantum advantage. To prove these results, we first show equivalence between deciding the value of an XOR game and solving an instance of the subgroup membership problem on a class of right angled Coxeter groups. We then show, in a proof that consumes most of this paper, that the instances of this problem corresponding to 3XOR games can be solved in polynomial time.