Pith Number

pith:BQCPQJQZ

pith:2026:BQCPQJQZ3UXYKZRWAJLQ6ZXCBE

not attested not anchored not stored refs pending

Synchronous Tunneling in a Multidimensional Quartic Potential: Competing Instanton Pathways and $D_4$ Symmetry Melting

M. Haashir Ismail, M. Mufassir, Pervez Hoodbhoy

In a quartic potential with four minima, competing instanton pathways drive a topological melting of discrete D4 symmetry into continuous O(2) symmetry at a critical coupling.

arxiv:2603.00652 v4 · 2026-02-28 · quant-ph · hep-th · math-ph · math.MP · nlin.PS · physics.chem-ph

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\usepackage{pith}
\pithnumber{BQCPQJQZ3UXYKZRWAJLQ6ZXCBE}

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Record completeness

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2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

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The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

We identify a critical coupling regime where the discrete D4 spatial symmetry of the minima undergoes a topological 'melting' transition into a continuous O(2) rotational symmetry.

C2weakest assumption

The dilute instanton gas approximation remains valid across the coupling range that includes the symmetry-melting point; the paper does not quantify the instanton density at which overlap corrections become important.

C3one line summary

Semi-classical analysis of a four-minima quartic potential identifies competing instanton pathways and a critical coupling at which D4 symmetry melts into O(2) rotational symmetry, yielding exact tunneling splittings validated by numerical diagonalization.

Receipt and verification

First computed	2026-05-20T00:03:07.102059Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0c04f82619dd2f85663602570f66e20905c29edb50d6e3c88a007cda53b87e17

Aliases

arxiv: 2603.00652 · arxiv_version: 2603.00652v4 · doi: 10.48550/arxiv.2603.00652 · pith_short_12: BQCPQJQZ3UXY · pith_short_16: BQCPQJQZ3UXYKZRW · pith_short_8: BQCPQJQZ

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/BQCPQJQZ3UXYKZRWAJLQ6ZXCBE \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 0c04f82619dd2f85663602570f66e20905c29edb50d6e3c88a007cda53b87e17

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "13200b5c4f0846b892c997754eece70cd47a1ab5e232d3d20240c1948fffc4ec",
    "cross_cats_sorted": [
      "hep-th",
      "math-ph",
      "math.MP",
      "nlin.PS",
      "physics.chem-ph"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "quant-ph",
    "submitted_at": "2026-02-28T13:44:21Z",
    "title_canon_sha256": "d07ae3c074531f02437cd207638f9c946b424f0c3f43f26f0701d7eb6ab20d71"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2603.00652",
    "kind": "arxiv",
    "version": 4
  }
}