Effective Lagrangian for Nonrelativistic Systems

Recent experimental developments in diverse areas -ranging from cold atomic gases to light-driven semiconductors to microcavity arrays -move systems into the focus which are located on the interface of quantum optics, many-body physics and statistical mechanics. They share in common that coherent and driven-dissipative quantum dynamics occur on an equal footing, creating genuine non-equilibrium scenarios without immediate counterpart in equilibrium condensed matter physics. This concerns both their non-thermal stationary states, as well as their many-body time evolution. It is a challenge to theory to identify novel instances of universal emergent macroscopic phenomena, which are tied unambiguously and in an observable way to the microscopic drive conditions. In this review, we discuss some recent results in this direction. Moreover, we provide a systematic introduction to the open system Keldysh functional integral approach, which is the proper technical tool to accomplish a merger of quantum optics and many-body physics, and leverages the power of modern quantum field theory to driven open quantum systems. CONTENTS

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“…The latter could be inferred along the lines of Refs. [220][221][222][223][224]. As we found in Sec.…”

Section: Spontaneous Symmetry Breaking and The Goldstone Theoremsupporting

confidence: 63%

Keldysh field theory for driven open quantum systems

2016

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“…In this work, we derive the weak-binding relation based on the low-energy effective field theory (EFT), which is a universal approach to extract the long-wavelength dynamics [27][28][29][30][31][32][33][34][35]. The EFT formulation provides much clear derivation of the weak binding relation in comparison with the original work [17].…”

Section: Introductionmentioning

confidence: 99%

Structure of near-threshold quasibound states

Kamiya

Hyodo

2016

Phys. Rev. C

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We study the compositeness of near-threshold quasi-bound states in the framework of effective field theory. From the viewpoint of the low-energy universality, we revisit the model-independent relations between the structure of the bound state and the observables in the weak binding limit. The effective field theory enables us to generalize the weak-binding relation of the stable bound states to unstable quasi-bound states with decay modes. We present the interpretation of the complex values of the compositeness for the unstable states. Combining the model-independent relation and the threshold observables extracted from the experimental data, we show that Λ(1405) is dominated by theKN molecular structure and that a0 (980) is dominated by the non-KK component.

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“…Much progress in SSB has also been achieved in the nonrelativistic cases, where the reduced spacetime symmetries allow a much richer behavior, still very much the subject of active research (see, e.g., Refs. [2][3][4][5][6][7][8] and the references therein). Important novelties emerge already in the simplest case of theories in the flat nonrelativistic spacetime R Dþ1 [covered with Cartesian coordinates ðt; xÞ, x ≡ ðx i ; i ¼ 1; …; DÞ] and with the Lifshitz symmetries of spatial rotations and spacetime translations.…”

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confidence: 98%

Cascading Multicriticality in Nonrelativistic Spontaneous Symmetry Breaking

2015

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Without Lorentz invariance, spontaneous global symmetry breaking can lead to multicritical NambuGoldstone modes with a higher-order low-energy dispersion ω ∼ k n (n ¼ 2; 3; …), whose naturalness is protected by polynomial shift symmetries. Here, we investigate the role of infrared divergences and the nonrelativistic generalization of the Coleman-Hohenberg-Mermin-Wagner (CHMW) theorem. We find novel cascading phenomena with large hierarchies between the scales at which the value of n changes, leading to an evasion of the "no-go" consequences of the relativistic CHMW theorem. DOI: 10.1103/PhysRevLett.115.241601 PACS numbers: 11.30.Qc, 11.10.Gh, 14.80.Va Some of the most pressing questions about the fundamental laws of the Universe (such as the cosmological constant problem or the hierarchy between the Higgs mass and the Planck scale) can be viewed as puzzles of technical naturalness [1]. In this Letter, we study the interplay of technical naturalness with spontaneous symmetry breaking (SSB) in nonrelativistic systems.SSB is ubiquitous in nature. For relativistic systems and global continuous internal symmetries, the universal features of SSB are controlled by the Goldstone theorem. Much progress in SSB has also been achieved in the nonrelativistic cases, where the reduced spacetime symmetries allow a much richer behavior, still very much the subject of active research (see, e.g., Refs. [2-8] and the references therein). Important novelties emerge already in the simplest case of theories in the flat nonrelativistic spacetime R Dþ1 [covered with Cartesian coordinates ðt; xÞ, x ≡ ðx i ; i ¼ 1; …; DÞ] and with the Lifshitz symmetries of spatial rotations and spacetime translations. In such theories, the Nambu-Goldstone (NG) modes can be either of two distinct types: type A, effectively described by a single real scalar ϕðt; xÞ with a kinetic term quadratic in the time derivatives; or type B, described by two scalar fields ϕ 1;2 ðt; xÞ which have a first-order kinetic term and thus form a canonical pair.In Refs. [7,8], we showed that this type A-B dichotomy is further refined into two discrete families, labeled by a positive integer n: type A n NG modes are described by a single scalar with dispersion ω ∼ k n (and dynamical critical exponent z ¼ n), while type B 2n modes are described by a canonical pair and exhibit the dispersion relation ω ∼ k 2n (and dynamical exponent z ¼ 2n). These two families are technically natural, and therefore stable under renormalization in the presence of interactions [7]. As usual, such naturalness is explained by a new symmetry. For n ¼ 1, the NG modes are protected by the well-known constant shift symmetry δϕðt; xÞ ¼ b. The n > 1 theories enjoy shift symmetries by a degree-P polynomial in the spatial coordinates [7] δϕðt;with a suitable P. Away from the type A n and B 2n Gaussian fixed points, the polynomial shift symmetry is generally broken by most interactions. The lowest, least irrelevant interaction terms invariant under the polynomial shift were systematically discussed in Ref...

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Effective Lagrangian for Nonrelativistic Systems

Cited by 116 publications

References 68 publications

Keldysh field theory for driven open quantum systems

Keldysh field theory for driven open quantum systems

Structure of near-threshold quasibound states

Cascading Multicriticality in Nonrelativistic Spontaneous Symmetry Breaking

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